Monochromatic paths and monochromatic sets of arcs in quasi-transitive digraphs

• Autorzy: Hortensia Galeana-Sánchez , R. Rojas-Monroy , B. Zavala
• Języki publikacji: EN

Abstrakty

EN

Let D be a digraph, V(D) and A(D) will denote the sets of vertices and arcs of D, respectively. We call the digraph D an m-coloured digraph if each arc of D is coloured by an element of {1,2,...,m} where m ≥ 1. 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 there is no monochromatic path between two vertices of N and if for every vertex v not in N there is a monochromatic path from v to some vertex in N. A digraph D is called a quasi-transitive digraph if (u,v) ∈ A(D) and (v,w) ∈ A(D) implies (u,w) ∈ A(D) or (w,u) ∈ A(D). We prove that if D is an m-coloured quasi-transitive digraph such that for every vertex u of D the set of arcs that have u as initial end point is monochromatic and D contains no C₃ (the 3-coloured directed cycle of length 3), then D has a kernel by monochromatic paths.

Słowa kluczowe

EN

m-coloured quasi-transitive digraph; kernel by monochromatic paths

Kategorie tematyczne

• 05C15: Coloring of graphs and hypergraphs
• 05C20: Directed graphs (digraphs), tournaments

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2010
• Tom: 30
• Numer: 4
• Strony: 545-553

Daty

wydano

2010

otrzymano

2007-05-21

poprawiono

2009-10-22

zaakceptowano

2009-10-27

Twórcy

autor

Hortensia Galeana-Sánchez

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, México

autor

R. Rojas-Monroy

• Facultad de Ciencias, Universidad Autónoma del Estado de México, Instituto Literario, Centro 50000, Toluca, Edo. de México, México

autor

B. Zavala

• Instituto de Matemáticas, Universidad Nacional Autónoma de México, Ciudad Universitaria, México, D.F. 04510, México

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Identyfikatory

DOI

10.7151/dmgt.1512