Discussiones Mathematicae Graph Theory 28(2) (2008)
285-306
doi: 10.7151/dmgt.1406
Hortensia Galeana-Sanchez
Instituto de Matemáticas |
Rocío Rojas-Monroy
Facultad de Ciencias |
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 it is proved that if D is an m-coloured bipartite tournament such that: every directed cycle of length 4 is quasi-monochromatic, every directed cycle of length 6 is monochromatic, and D has no induced particular 6-element bipartite tournament T^{˜}_{6}, then D has a kernel by monochromatic paths.
Keywords: kernel, kernel by monochromatic paths, bipartite tournament.
2000 Mathematics Subject Classification: 05C20.
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Received 6 July 2007
Revised 10 April 2008
Accepted 10 April 2008