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H-Kernels in Infinite Digraphs

✍ Scribed by Galeana-Sánchez, Hortensia; Sánchez-López, Rocío

Book ID
117994768
Publisher
Springer Japan
Year
2012
Tongue
English
Weight
189 KB
Volume
29
Category
Article
ISSN
0911-0119

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We call the digraph D an m-coloured digraph if the arcs of D are coloured with m colours. A directed path is called monochromatic if all of its arcs are coloured alike. A directed cycle is called quasi-monochromatic if with at most one exception all of its arcs are coloured alike. A set N C\_\_ V(D)

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## Abstract A __quasi‐kernel__ in a digraph is an independent set of vertices such that any vertex in the digraph can reach some vertex in the set via a directed path of length at most two. Chvátal and Lovász proved that every digraph has a quasi‐kernel. Recently, Gutin et al. raised the question o