ArticleOriginal scientific text
Title
Monochromatic paths and monochromatic sets of arcs in 3-quasitransitive digraphs
Authors 1, 2, 1
Affiliations
- Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, México
- Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario, Centro 50000, Toluca, Edo. de México, México
Abstract
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 set N of vertices of D is called a kernel by monochromatic paths if for every pair of vertices of N there is no monochromatic path between them and for every vertex v ∉ N there is a monochromatic path from v to N. We denote by A⁺(u) the set of arcs of D that have u as the initial vertex. We prove that if D is an m-coloured 3-quasitransitive digraph such that for every vertex u of D, A⁺(u) is monochromatic and D satisfies some colouring conditions over one subdigraph of D of order 3 and two subdigraphs of D of order 4, then D has a kernel by monochromatic paths.
Keywords
m-coloured digraph, 3-quasitransitive digraph, kernel by monochromatic paths, γ-cycle, quasi-monochromatic digraph
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Pages:
337-347
Main language of publication
English
Received
2007-11-06
Accepted
2009-02-26
Published
2009
DOI: 10.7151/dmgt.1450
Exact and natural sciences