eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1027
1038
862
Forced oscillations of a damped Korteweg-de Vries equation on a periodic domain
M. Chen
chenmochenmo.good@163.com
1
School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun 130024, P. R. China.
In this paper, we investigate a damped Korteweg-de Vries equation with forcing on a periodic domain $\mathbb{T}=\mathbb{R}/(2\pi\mathbb{Z})$. We can obtain that if the forcing is periodic with small amplitude, then the solution becomes eventually time-periodic.
http://bims.iranjournals.ir/article_862_ab038992016b1b175d32df688062e53c.pdf
Forced oscillation
Korteweg-de Vries equation
stability
time-periodic solution
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1039
1057
863
Boundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method
M. Garshasbi
m_garshasbi@iust.ac.ir
1
F. Hassani
hasani_fh@yahoo.com
2
School of Mathematics, Iran University of Science and Technology, Tehran, Iran.
School of Mathematics, Iran University of Science and Technology, Tehran, Iran.
In this paper, we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linear algebraic equations is ill-posed, the Tikhonov first-order regularization procedure is employed to obtain a stable solution. Determination of regularization parameter is based on L-curve technique. Some numerical examples for the feasibility of the proposed method are presented.
http://bims.iranjournals.ir/article_863_d469ccbf86a94e4c4831982ef32f13b6.pdf
Inverse boundary problem
heat equation
boundary integral equation method
regularization.
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1057
1076
864
On a generalization of condition (PWP)
X. Liang
lxl_119@126.com
1
Y. Luo
luoyf@lzu.edu.cn
2
Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China.
Department of Mathematics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China.
There is a flatness property of acts over monoids called Condition $(PWP)$ which, so far, has received much attention. In this paper, we introduce Condition GP-$(P)$, which is a generalization of Condition $(PWP)$. Firstly, some characterizations of monoids by Condition GP-$(P)$ of their (cyclic, Rees factor) acts are given, and many known results are generalized. Moreover, some possible conditions on monoids that describe when their diagonal acts satisfy Condition GP-$(P)$ are found. Finally, using some new types of epimorphisms, an alternative description of Condition GP-$(P)$ (resp., Condition $(PWP)$) is obtained, and directed colimits of these new epimorphisms are investigated.
http://bims.iranjournals.ir/article_864_6aca97cc012989be8545639bb27655ed.pdf
$S$-act
Condition $(PWP)$
condition GP-$(P)$
generally left right ideal
quasi G-2-pure epimorphism
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1077
1086
865
Approximate solution of dual integral equations
S. Ahdiaghdam
ahdi@marandiau.ac.ir
1
K. Ivaz
ivaz@tabrizu.ac.ir
2
S. Shahmorad
shahmorad@tabrizu.ac.ir
3
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
We study dual integral equations which appear in formulation of the potential distribution of an electrified plate with mixed boundary conditions. These equations will be converted to a system of singular integral equations with Cauchy type kernels. Using Chebyshev polynomials, we propose a method to approximate the solution of Cauchy type singular integral equation which will be used to approximate the solution of the main dual integral equations. Numerical results demonstrate effectiveness of this method.
http://bims.iranjournals.ir/article_865_36fdbd67705679576cbc4c02707cf62d.pdf
Dual integral equation
Cauchy type integral equation
Fourier transform
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1087
1096
866
On the bounds in Poisson approximation for independent geometric distributed random variables
T. L. Hung
tlhung@ufm.edu.vn
1
L. T. Giang
ltgiang@ufm.edu.vn
2
University of Finance and Marketing, 2/4 Tran Xuan Soan, District 7, Ho Chi Minh city, Vietnam.
University of Finance and Marketing, 2/4 Tran Xuan Soan, District 7, Ho Chi Minh city, Vietnam.
The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method. Some results related to random sums of independent geometric distributed random variables are also investigated.
http://bims.iranjournals.ir/article_866_5fccc709565917424a38a1fa4d5c23c3.pdf
Poisson approximation
linear operator
geometric random variable
random sums
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1097
1106
867
Which elements of a finite group are non-vanishing?
M. Arezoomand
arezoomand@math.iut.ac.ir
1
B. Taeri
b.taeri@cc.iut.ac.ir
2
Department of Mathematical Sciences, Isfahan University of Technology, P.O. Box 84156-83111, Isfahan, Iran.
Department of Mathematical Sciences, Isfahan University of Technology, P.O. Box 84156-838111, Isfahan, Iran.
Let $G$ be a finite group. An element $g\in G$ is called non-vanishing, if for every irreducible complex character $\chi$ of $G$, $\chi(g)\neq 0$. The bi-Cayley graph ${\rm BCay}(G,T)$ of $G$ with respect to a subset $T\subseteq G$, is an undirected graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(tx,2)\}\mid x\in G, \ t\in T\}$. Let ${\rm nv}(G)$ be the set of all non-vanishing elements of a finite group $G$. We show that $g\in nv(G)$ if and only if the adjacency matrix of ${\rm BCay}(G,T)$, where $T={\rm Cl}(g)$ is the conjugacy class of $g$, is non-singular. We prove that if the commutator subgroup of $G$ has prime order $p$, then (1) $g\in {\rm nv}(G)$ if and only if $|Cl(g)|<p$, (2) if $p$ is the smallest prime divisor of $|G|$, then ${\rm nv}(G)=Z(G)$. Also we show that (a) if ${\rm Cl}(g)=\{g,h\}$, then $g\in {\rm nv}(G)$ if and only if $gh^{-1}$ has odd order, (b) if $|{\rm Cl}(g)|\in \{2,3\}$ and $({\rm ord}(g),6)=1$, then $g\in {\rm nv}(G)$.
http://bims.iranjournals.ir/article_867_e6b164bbe3a5bd8febacd1a5524efcc6.pdf
Non-vanishing element
character
conjugacy class
Bi-Cayley graph
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1107
1126
868
Numerical approach for solving a class of nonlinear fractional differential equation
S. Irandoust-pakchin
s.irandoust@tabrizu.ac.ir
1
M. Lakestani
lakestani@tabrizu.ac.ir
2
H. Kheiri
h-kheiri@tabrizu.ac.ir
3
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran.
It is commonly accepted that fractional differential equations play an important role in the explanation of many physical phenomena. For this reason we need a reliable and efficient technique for the solution of fractional differential equations. This paper deals with the numerical solution of a class of fractional differential equation. The fractional derivatives are described based on the Caputo sense. Our main aim is to generalize the Chebyshev cardinal operational matrix to the fractional calculus. In this work, the Chebyshev cardinal functions together with the Chebyshev cardinal operational matrix of fractional derivatives are used for numerical solution of a class of fractional differential equations. The main advantage of this approach is that it reduces fractional problems to a system of algebraic equations. The method is applied to solve nonlinear fractional differential equations. Illustrative examples are included to demonstrate the validity and applicability of the presented technique.
http://bims.iranjournals.ir/article_868_26827a7d21fe2b110ccd0dc9c647f92a.pdf
Fractional-order differential equation
operational matrix of fractional derivative
Caputo derivative
Chebyshev cardinal function
collocation method
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1127
1142
869
The use of inverse quadratic radial basis functions for the solution of an inverse heat problem
F. Parzlivand
fparzlivand@gmail.com
1
A. Shahrezaee
ashahrezaee@alzahra.ac.ir
2
Department of Mathematics, Alzahra University, Vanak, Post Code 19834, Tehran, Iran.
Department of Mathematics, Alzahra University, Vanak, Post Code 19834, Tehran, Iran.
In this paper, a numerical procedure for an inverse problem of simultaneously determining an unknown coefficient in a semilinear parabolic equation subject to the specification of the solution at an internal point along with the usual initial boundary conditions is considered. The method consists of expanding the required approximate solution as the elements of the inverse quadratic radial basis functions (IQ-RBFs). The operational matrix of derivative for IQ-RBFs is introduced and the new computational technique is used for this purpose. The operational matrix of derivative is utilized to reduce the problem to a set of algebraic equations. Some examples are given to demonstrate the validity and applicability of the new method and a comparison is made with the existing results.
http://bims.iranjournals.ir/article_869_56874af181e3b46e92db683c4c49a920.pdf
Collocation
inverse parabolic problem
scattered data
RBFs
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1143
1154
870
Composition operators and natural metrics in meromorphic function classes $Q_p$
A. Kamal
alaa_mohamed1@yahoo.com
1
Port Said University, Faculty of Science, Department of Mathematics, Port Said 42521, Egypt.
In this paper, we investigate some results on natural metrics on the $\mu$-normal functions and meromorphic $Q_p$-classes. Also, these classes are shown to be complete metric spaces with respect to the corresponding metrics. Moreover, compact composition operators $C_\phi$ and Lipschitz continuous operators acting from $\mu$-normal functions to the meromorphic $Q_p$-classes are characterized by conditions depending only on $\phi.$
http://bims.iranjournals.ir/article_870_35e24f164aba15e6073c999fba0d70b5.pdf
Meromorphic classes
composition operators
Lipschitz continuous
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1155
1167
871
Multiplication operators on Banach modules over spectrally separable algebras
J. Bračič
janko.bracic@fmf.uni-lj.si
1
Department of Materials and Metallurgy, Faculty of Natural Sciences and Engineering, University of Ljubljana, Aškerčeva c. 12, SI-1000 Ljubljana, Slovenia.
Let $\mathcal{A}$ be a commutative Banach algebra and $\mathscr{X}$ be a left Banach $\mathcal{A}$-module. We study the set ${\rm Dec}_{\mathcal{A}}(\mathscr{X})$ of all elements in $\mathcal{A}$ which induce a decomposable multiplication operator on $\mathscr{X}$. In the case $\mathscr{X}=\mathcal{A}$, ${\rm Dec}_{\mathcal{A}}(\mathcal{A})$ is the well-known Apostol algebra of $\mathcal{A}$. We show that ${\rm Dec}_{\mathcal{A}}(\mathscr{X})$ is intimately related with the largest spectrally separable subalgebra of $\mathcal{A}$ and in this context we give some results which are related to an open question if Apostol algebra is regular for any commutative algebra $\mathcal{A}$.
http://bims.iranjournals.ir/article_871_9f5eadc32836600803a25c1fd5936d46.pdf
Commutative Banach algebra
decomposable multiplication operator
spectrally separable algebra
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1169
1177
872
On a functional equation for symmetric linear operators on $C^{*}$ algebras
A. Taghavi
taghavi@du.ac.ir
1
Faculty of Mathematics and Computer Science, Damghan University, Damghan, Iran.
Let $A$ be a $C^{*}$ algebra, $T: A\rightarrow A$ be a linear map which satisfies the functional equation $T(x)T(y)=T^{2}(xy),\;\;T(x^{*})=T(x)^{*} $. We prove that under each of the following conditions, $T$ must be the trivial map $T(x)=\lambda x$ for some $\lambda \in \mathbb{R}$: i) $A$ is a simple $C^{*}$-algebra. ii) $A$ is unital with trivial center and has a faithful trace such that each zero-trace element lies in the closure of the span of commutator elements. iii) $A=B(H)$ where $H$ is a separable Hilbert space. For a given field $F$, we consider a similar functional equation {$ T(x)T(y) =T^{2}(xy), T(x^{tr})=T(x)^{tr}, $} where $T$ is a linear map on $M_{n}(F)$ and "tr" is the transpose operator. We prove that this functional equation has trivial solution for all $n\in \mathbb{N}$ if and only if $F$ is a formally real field.
http://bims.iranjournals.ir/article_872_fd7287eb7f1365d9156e9da3ccb25196.pdf
"Functional Equations"
"$C^{*}$ algebras"
" Formally real fields"
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1179
1195
873
The Fischer-Clifford matrices and character table of the maximal subgroup $2^9{:}(L_3(4){:}S_3)$ of $U_6(2){:}S_3$
A. L. Prins
abraham.prins@ma2.sun.ac.za
1
Department of Mathematics, Faculty of Military Science, Stellenbosch University, Private Bag X2, Saldanha, 7395, South Africa.
The full automorphism group of $U_6(2)$ is a group of the form $U_6(2){:}S_3$. The group $U_6(2){:}S_3$ has a maximal subgroup $2^9{:}(L_3(4){:}S_3)$ of order 61931520. In the present paper, we determine the Fischer-Clifford matrices (which are not known yet) and hence compute the character table of the split extension $2^9{:}(L_3(4){:}S_3)$.
http://bims.iranjournals.ir/article_873_6ec8116653a7fc6145c53dd9e3228b5f.pdf
Coset analysis
Fischer-Clifford matrices
permutation character
fusion map
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-11-01
42
5
1197
1206
874
Some commutativity theorems for $*$-prime rings with $(\sigma,\tau)$-derivation
M. Ashraf
mashraf80@hotmail.com
1
N. Parveen
naziamath@gmail.com
2
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India.
Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India.
Let $R$ be a $*$-prime ring with center $Z(R)$, $d$ a non-zero $(\sigma,\tau)$-derivation of $R$ with associated automorphisms $\sigma$ and $\tau$ of $R$, such that $\sigma$, $\tau$ and $d$ commute with $'*'$. Suppose that $U$ is an ideal of $R$ such that $U^*=U$, and $C_{\sigma,\tau}=\{c\in R~|~c\sigma(x)=\tau(x)c~\mbox{for~all}~x\in R\}.$ In the present paper, it is shown that if characteristic of $R$ is different from two and $[d(U),d(U)]_{\sigma,\tau}=\{0\},$ then $R$ is commutative. Commutativity of $R$ has also been established in case if $[d(R),d(R)]_{\sigma,\tau}\subseteq C_{\sigma,\tau}.$
http://bims.iranjournals.ir/article_874_0ec3eca69c4da52c1cf3357568f2b7fd.pdf
Prime-rings
derivations
ideal
involution map
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1207
1219
875
Common solutions to pseudomonotone equilibrium problems
D. V. Hieu
dv.hieu83@gmail.com
1
Department of Mathematics, Ha Noi University of Science, VNU. 334, Nguyen Trai Street, Ha Noi, Vietnam.
In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from the previously known one for variational inequalities to equilibrium problems. The second is a new cyclic hybrid extragradient-cutting algorithm. In the cyclic algorithm, using the known techniques, we can perform and develop practical numerical experiments.
http://bims.iranjournals.ir/article_875_e39c67b7360a9dceda155977e3771762.pdf
Hybrid method
parallel algorithm
cyclic algorithm
extragradient method
equilibrium problem
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1221
1235
876
$\mathcal{X}$-injective and $\mathcal{X}$-projective complexes
T. Özen
ozen_t@ibu.edu.tr
1
E. Yıldırım
emineyyildirim@gmail.com
2
Department of Mathematics, Abant Izzet Baysal University, Gölköy Kampüsü Bolu, Turkey.
Department of Mathematics, Abant Izzet Baysal University, Gölköy Kampüsü Bolu, Turkey.
Let $\mathcal{X}$ be a class of $R$-modules. In this paper, we investigate \;$\mathcal{X}$-injective (projective) and DG-$\mathcal{X}$-injective (projective) complexes which are generalizations of injective (projective) and DG-injective (projective) complexes. We prove that some known results can be extended to the class of \;$\mathcal{X}$-injective (projective) and DG-$\mathcal{X}$-injective (projective) complexes for this general settings.
http://bims.iranjournals.ir/article_876_bcc953321d1ed4f3a9c517d160fe4c40.pdf
Injective (Projective) complex
precover
preenvelope
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1237
1246
877
Sufficient global optimality conditions for general mixed integer nonlinear programming problems
J. Quan
quanjingcq@163.com
1
Z. Y. Wu
zhiyouwu@263.net
2
G. Q. Li
ligq@cqnu.edu.cn
3
Department of Mathematics, Yibin University, Yibin, Sichuan, 644007, China.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China.
School of Mathematical Sciences, Chongqing Normal University, Chongqing 401331, China.
In this paper, some KKT type sufficient global optimality conditions for general mixed integer nonlinear programming problems with equality and inequality constraints (MINPP) are established. We achieve this by employing a Lagrange function for MINPP. In addition, verifiable sufficient global optimality conditions for general mixed integer quadratic programming problems are derived easily. Numerical examples are also presented.
http://bims.iranjournals.ir/article_877_e02f8f1f336deb5527f980f598eefbff.pdf
Sufficient global optimality conditions
mixed integer nonlinear programming
mixed integer quadratic programming
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1247
1258
878
A note on Fouquet-Vanherpe’s question and Fulkerson conjecture
F. Chen
chenfuyuan19871010@163.com
1
Institute of Statistics and Applied Mathematics, Anhui University of Finance and Economics, Bengbu, Anhui, 233030, P. R. China.
The excessive index of a bridgeless cubic graph $G$ is the least integer $k$, such that $G$ can be covered by $k$ perfect matchings. An equivalent form of Fulkerson conjecture (due to Berge) is that every bridgeless cubic graph has excessive index at most five. Clearly, Petersen graph is a cyclically 4-edge-connected snark with excessive index at least 5, so Fouquet and Vanherpe asked whether Petersen graph is the only one with that property. H\"{a}gglund gave a negative answer to their question by constructing two graphs Blowup$(K_4, C)$ and Blowup$(Prism, C_4)$. Based on the first graph, Esperet et al. constructed infinite families of cyclically 4-edge-connected snarks with excessive index at least five. Based on these two graphs, we construct infinite families of cyclically 4-edge-connected snarks $E_{0,1,2,\ldots, (k-1)}$ in which $E_{0,1,2}$ is Esperet et al.'s construction. In this note, we prove that $E_{0,1,2,3}$ has excessive index at least five, which gives a strongly negative answer to Fouquet and Vanherpe's question. As a subcase of Fulkerson conjecture, H\"{a}ggkvist conjectured that every cubic hypohamiltonian graph has a Fulkerson-cover. Motivated by a related result due to Hou et al.'s, in this note we prove that Fulkerson conjecture holds on some families of bridgeless cubic graphs.
http://bims.iranjournals.ir/article_878_1c321310c71687bcfea04de293b6da0f.pdf
Fulkerson-cover
excessive index
snark
hypohamiltonian graph
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1259
1277
879
Operator-valued tensors on manifolds
H. Feizabadi
hassan_feiz1970@aut.ac.ir
1
N. Boroojerdian
broojerd@aut.ac.ir
2
Faculty of Mathematics & Computer Science, Amirkabir University of Technology, Tehran, Iran.
Faculty of Mathematics \& Computer Science, Amirkabir University of Technology, Tehran, Iran.
In this paper we try to extend geometric concepts in the context of operator valued tensors. To this end, we aim to replace the field of scalars $ \mathbb{R} $ by self-adjoint elements of a commutative $ C^\star $-algebra, and reach an appropriate generalization of geometrical concepts on manifolds. First, we put forward the concept of operator-valued tensors and extend semi-Riemannian metrics to operator valued metrics. Then, in this new geometry, some essential concepts of Riemannian geometry such as curvature tensor, Levi-Civita connection, Hodge star operator, exterior derivative, divergence,... will be considered.
http://bims.iranjournals.ir/article_879_44f3202eefb900362bb1960d135193a5.pdf
Operator-valued tensors
operator-valued semi-Riemannian metrics
Levi-Civita connection
curvature
Hodge star operator
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1279
1291
880
Irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$
T. Le
lttung96@yahoo.com
1
Mathematics Department, North-West University, Mafikeng, South Africa.
Here we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.
http://bims.iranjournals.ir/article_880_35a9b44674a8153d0f083d3be4621a0b.pdf
Irreducible character
root system
Sylow subgroup
Steinberg triality
eng
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
2016-10-01
42
5
1293
1303
881
On list vertex 2-arboricity of toroidal graphs without cycles of specific length
H. Zhang
hhzh@hytc.edu.cn
1
School of Mathematical Science, Huaiyin Normal University, 111 Changjiang West Road, Huaian, Jiangsu, 223300, P. R. China.
The vertex arboricity $\rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph. A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$, one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by every color class is a forest. The smallest $k$ for a graph to be list vertex $k$-arborable is denoted by $\rho_l(G)$. Borodin, Kostochka and Toft (Discrete Math. 214 (2000) 101-112) first introduced the list vertex arboricity of $G$. In this paper, we prove that $\rho_l(G)\leq 2$ for any toroidal graph without 5-cycles. We also show that $\rho_l(G)\leq 2$ if $G$ contains neither adjacent 3-cycles nor cycles of lengths 6 and 7.
http://bims.iranjournals.ir/article_881_1c2751a2e851f892b91c1fd5de3e21f4.pdf
Vertex arboricity
toroidal graph
structure
cycle