Kernels by properly colored paths in arc-colored digraphs
Combinatorics
2017-04-28 v1
Abstract
A {\em kernel by properly colored paths} of an arc-colored digraph is a set of vertices of such that (i) no two vertices of are connected by a properly colored directed path in , and (ii) every vertex outside can reach by a properly colored directed path in . In this paper, we conjecture that every arc-colored digraph with all cycles properly colored has such a kernel and verify the conjecture for unicyclic digraphs, semi-complete digraphs and bipartite tournaments, respectively. Moreover, weaker conditions for the latter two classes of digraphs are given.
Keywords
Cite
@article{arxiv.1704.08455,
title = {Kernels by properly colored paths in arc-colored digraphs},
author = {Yandong Bai and Shinya Fujita and Shenggui Zhang},
journal= {arXiv preprint arXiv:1704.08455},
year = {2017}
}