@article {
author = {Bagheri Gh., B. and Omoomi, B.},
title = {On the oriented perfect path double cover conjecture},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {41},
number = {1},
pages = {189-200},
year = {2015},
publisher = {Springer and the Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {An oriented perfect path double cover (OPPDC) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each arc of $G_s$ lies in exactly one of the paths and each vertex of $G$ appears just once as a beginning and just once as an end of a path. Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete Math. 276 (2004) 287-294) conjectured that every graph except two complete graphs $K_3$ and $K_5$ has an OPPDC and they claimed that the minimum degree of the minimal counterexample to this conjecture is at least four. In the proof of their claim, when a graph is smaller than the minimal counterexample, they missed to consider the special cases $K_3$ and $K_5$. In this paper, among some other results, we present the complete proof for this fact. Moreover, we prove that the minimal counterexample to this conjecture is $2$-connected and $3$-edge-connected.},
keywords = {Keywords: Oriented perfect,path double cover,Oriented cycle
double cover},
url = {http://bims.iranjournals.ir/article_597.html},
eprint = {http://bims.iranjournals.ir/article_597_a931117b555271ee48028056b0d0101b.pdf}
}