@article {
author = {Zhang, H.},
title = {On list vertex 2-arboricity of toroidal graphs without cycles of specific length},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {42},
number = {5},
pages = {1293-1303},
year = {2016},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {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.},
keywords = {Vertex arboricity,toroidal graph,structure,cycle},
url = {http://bims.iranjournals.ir/article_881.html},
eprint = {http://bims.iranjournals.ir/article_881_1c2751a2e851f892b91c1fd5de3e21f4.pdf}
}