Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8902958 | Discrete Mathematics | 2018 | 11 Pages |
Abstract
A kernel by properly colored paths of an arc-colored digraph D is a set S of vertices of D such that (i) no two vertices of S are connected by a properly colored directed path in D, and (ii) every vertex outside S can reach S by a properly colored directed path in D. In this paper, we conjecture that every arc-colored digraph with all cycles properly colored has such a kernel and verify the conjecture for digraphs with no intersecting cycles, semi-complete digraphs and bipartite tournaments, respectively. Moreover, weaker conditions for the latter two classes of digraphs are given.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Yandong Bai, Shinya Fujita, Shenggui Zhang,