On monochromatic paths in edge-coloured digraphs
TLDR
It is proved that if G contains no monochromatic infinite outward path, then there is an independent set S of vertices of G such that, for every vertex x not in S, there is a monochromaatic directed path from x to a vertex of S.About:
This article is published in Journal of Combinatorial Theory, Series B.The article was published on 1982-12-01 and is currently open access. It has received 131 citations till now. The article focuses on the topics: Neighbourhood (graph theory) & Distance.read more
Citations
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A fixed-point approach to stable matchings and some applications
TL;DR: A matroid-generalization of the stable marriage theorem is formulated and results of Vande Vate and Rothblum are extended on the bipartite stable matching polytope and the lattice structure of generalized stable matchings are studied.
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Cycles and paths in semicomplete multipartite digraphs, theorems, and algorithms: a survey
TL;DR: Results (theorems and algorithms) on directed walks in semicomplete m- partite digraphs are described including some recent results concerning tournaments.
Journal Article
On monochromatic paths in m -coloured tournaments
TL;DR: It is proved that if T is an m -coloured tournament which does not contain any tournament of order 3 whose arcs are coloured with three distinct colours then there is a vertex v of T such that for every other vertex x of Tthere is a monochromatic path from x to v.
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On monochromatic paths in m-coloured tournaments
TL;DR: In this paper, it was shown that if a tournament T is an m -coloured tournament which does not contain any tournament of order 3 whose arcs are coloured with three distinct colours, then there is a vertex v of T such that for every other vertex x of T there is an monochromatic path from x to v.
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On monochromatic paths and monochromatic cycles in edge coloured tournaments
TL;DR: Some sufficient conditions are obtained for an m -coloured tournament T to have a vertex v such that for every other vertex x of T there is a monochromatic directed path from x to v.
References
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On dominance relations and the structure of animal societies: III The condition for a score structure
TL;DR: The necessary and sufficient condition for n integers to be the score structure of a society with a dominance relation is given in this article, where the necessary and necessary condition is given forn integers.