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An anti-Ramsey theorem on edge-cuts

100%

Montellano-Ballesteros J.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 1

19-21

Let G = (V(G), E(G)) be a connected multigraph and let h(G) be the minimum integer k such that for every edge-colouring of G, using exactly k colours, there is at least one edge-cut of G all of whose edges receive different colours. In this note it is proved that if G has at least 2 vertices and has no bridges, then h(G) = |E(G)| -|V(G)| + 2.

Independent transversals of longest paths in locally semicomplete and locally transitive digraphs

51%

Galeana-Sánchez H., Gómez R., Montellano-Ballesteros J.

Discussiones Mathematicae Graph Theory

2009

tom 29

nr 3

469-480

We present several results concerning the Laborde-Payan-Xuang conjecture stating that in every digraph there exists an independent set of vertices intersecting every longest path. The digraphs we consider are defined in terms of local semicompleteness and local transitivity. We also look at oriented graphs for which the length of a longest path does not exceed 4.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

2 Montellano-Ballesteros J.

1 Galeana-Sánchez H.

1 Gómez R.

1 2009

1 2006

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An anti-Ramsey theorem on edge-cuts

Independent transversals of longest paths in locally semicomplete and locally transitive digraphs