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(k,l)-kernels in line digraphs

✍ Scribed by Qin Lu; Er-fang Shan; Min Zhao

Book ID
107482368
Publisher
Chinese Electronic Periodical Services
Year
2006
Tongue
English
Weight
244 KB
Volume
10
Category
Article
ISSN
1007-6417

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In this paper we present some results on the existence of /c-kernels and (k, [)-kernels in digraphs which generalize the following Theorem of P. Duchet [2]: "If every directed cycle of odd length in a digraph D has at least two symmetrical arcs, then D has a kernel.

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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. ChvΓ‘tal and LovΓ‘sz proved that every digraph has a quasi‐kernel. Recently, Gutin et al. raised the question o

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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)