Odd 2-factored snarks
Combinatorics
2015-01-13 v2 Discrete Mathematics
Abstract
A {\em snark} is a cubic cyclically 4-edge connected graph with edge chromatic number four and girth at least five. We say that a graph is {\em odd 2-factored} if for each 2-factor F of G each cycle of F is odd. In this paper, we present a method for constructing odd 2--factored snarks. In particular, we construct two families of odd 2-factored snarks that disprove a conjecture by some of the authors. Moreover, we approach the problem of characterizing odd 2-factored snarks furnishing a partial characterization of cyclically 4-edge connected odd 2-factored snarks. Finally, we pose a new conjecture regarding odd 2-factored snarks.
Keywords
Cite
@article{arxiv.1210.8101,
title = {Odd 2-factored snarks},
author = {M. Abreu and D. Labbate and R. Rizzi and J. Sheehan},
journal= {arXiv preprint arXiv:1210.8101},
year = {2015}
}