Odd Properly Colored Cycles in Edge-Colored Graphs
Combinatorics
2016-05-02 v1
Abstract
It is well-known that an undirected graph has no odd cycle if and only if it is bipartite. A less obvious, but similar result holds for directed graphs: a strongly connected digraph has no odd cycle if and only if it is bipartite. Can this result be further generalized to more general graphs such as edge-colored graphs? In this paper, we study this problem and show how to decide if there exists an odd properly colored cycle in a given edge-colored graph. As a by-product, we show how to detect if there is a perfect matching in a graph with even (or odd) number of edges in a given edge set.
Keywords
Cite
@article{arxiv.1604.08851,
title = {Odd Properly Colored Cycles in Edge-Colored Graphs},
author = {Gregory Gutin and Bin Sheng and Magnus Wahlström},
journal= {arXiv preprint arXiv:1604.08851},
year = {2016}
}