Year: 2012
Type: preprint
Abstract: An {\sf oriented perfect path double cover} ($\rm OPPDC$) of a graph $G$ is a collection of directed paths in the symmetric orientation $G_s$ of $G$ such that each edge 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{á} and Ne{š}et{ř}il (Discrete Math. 276 (2004) 287-294) conjectured that every graph except two complete graphs $K_3$ and $K_5$ has an $\rm OPPDC$ and they proved that the minimum degree of the minimal counterexample to this conjecture is at least four. In this paper, among some other results, we prove that the minimal counterexample to this conjecture is 2-connected and 3-edge-connected.
Source: arXiv (Cornell University)
Authors: Gh., Behrooz Bagheri, Omoomi, Behnaz
Institution: Isfahan University of Technology
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951095055