Displaying similar documents to “Long heterochromatic paths in edge-colored graphs.”

On kernels by monochromatic paths in the corona of digraphs

Iwona Włoch (2008)

Open Mathematics

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In this paper we derive necessary and sufficient conditions for the existence of kernels by monochromatic paths in the corona of digraphs. Using these results, we are able to prove the main result of this paper which provides necessary and sufficient conditions for the corona of digraphs to be monochromatic kernel-perfect. Moreover we calculate the total numbers of kernels by monochromatic paths, independent by monochromatic paths sets and dominating by monochromatic paths sets in this...

Paths through fixed vertices in edge-colored graphs

W. S. Chou, Y. Manoussakis, O. Megalakaki, M. Spyratos, Zs. Tuza (1994)

Mathématiques et Sciences Humaines

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We study the problem of finding an alternating path having given endpoints and passing through a given set of vertices in edge-colored graphs (a path is alternating if any two consecutive edges are in different colors). In particular, we show that this problem in NP-complete for 2-edge-colored graphs. Then we give a polynomial characterization when we restrict ourselves to 2-edge-colored complete graphs. We also investigate on (s,t)-paths through fixed vertices, i.e. paths of length...

Characterizations of Graphs Having Large Proper Connection Numbers

Chira Lumduanhom, Elliot Laforge, Ping Zhang (2016)

Discussiones Mathematicae Graph Theory

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Let G be an edge-colored connected graph. A path P is a proper path in G if no two adjacent edges of P are colored the same. If P is a proper u − v path of length d(u, v), then P is a proper u − v geodesic. An edge coloring c is a proper-path coloring of a connected graph G if every pair u, v of distinct vertices of G are connected by a proper u − v path in G, and c is a strong proper-path coloring if every two vertices u and v are connected by a proper u− v geodesic in G. The minimum...

γ-Cycles And Transitivity By Monochromatic Paths In Arc-Coloured Digraphs

Enrique Casas-Bautista, Hortensia Galeana-Sánchez, Rocío Rojas-Monroy (2013)

Discussiones Mathematicae Graph Theory

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We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. If D is an m-coloured digraph and a ∈ A(D), colour(a) will denote the colour has been used on a. A path (or a cycle) is called monochromatic if all of its arcs are coloured alike. A γ-cycle in D is a sequence of vertices, say γ = (u0, u1, . . . , un), such that ui ≠ uj if i ≠ j and for every i ∈ 0, 1, . . . , n there is a uiui+1-monochromatic path in D and there is no ui+1ui-monochromatic path in D (the...