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- W2021340270 abstract "We call the digraph D an k-colored digraph if the arcs of D are colored with k colors. A subdigraph H of D is called monochromatic if all of its arcs are colored alike. A set N⊆V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions: (i) for every pair of different vertices u,v∈N, there is no monochromatic directed path between them, and (ii) for every vertex x∈(V(D)∖N), there is a vertex y∈N such that there is an xy-monochromatic directed path. In this paper, we prove that if D is an k-colored digraph that can be partitioned into two vertex-disjoint transitive tournaments such that every directed cycle of length 3,4 or 5 is monochromatic, then D has a kernel by monochromatic paths. This result gives a positive answer (for this family of digraphs) of the following question, which has motivated many results in monochromatic kernel theory: Is there a natural number l such that if a digraph D is k-colored so that every directed cycle of length at most l is monochromatic, then D has a kernel by monochromatic paths?" @default.
- W2021340270 created "2016-06-24" @default.
- W2021340270 creator A5029325738 @default.
- W2021340270 creator A5035539781 @default.
- W2021340270 date "2011-07-01" @default.
- W2021340270 modified "2023-10-18" @default.
- W2021340270 title "Kernels by monochromatic paths in digraphs with covering number 2" @default.
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- W2021340270 doi "https://doi.org/10.1016/j.disc.2010.09.022" @default.
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