Kernels by Monochromatic Paths and Color-Perfect Digraphs

• Autorzy: Hortensia Galeana-Śanchez , Rocío Sánchez-López
• Języki publikacji: EN

Abstrakty

EN

For a digraph D, V (D) and A(D) will denote the sets of vertices and arcs of D respectively. In an arc-colored digraph, a subset K of V(D) is said to be kernel by monochromatic paths (mp-kernel) if (1) for any two different vertices x, y in N there is no monochromatic directed path between them (N is mp-independent) and (2) for each vertex u in V (D) \ N there exists v ∈ N such that there is a monochromatic directed path from u to v in D (N is mp-absorbent). If every arc in D has a different color, then a kernel by monochromatic paths is said to be a kernel. Two associated digraphs to an arc-colored digraph are the closure and the color-class digraph CC(D). In this paper we will approach an mp-kernel via the closure of induced subdigraphs of D which have the property of having few colors in their arcs with respect to D. We will introduce the concept of color-perfect digraph and we are going to prove that if D is an arc-colored digraph such that D is a quasi color-perfect digraph and CC(D) is not strong, then D has an mp-kernel. Previous interesting results are generalized, as for example Richardson′s Theorem.

Słowa kluczowe

EN

kernel; kernel perfect digraph; kernel by monochromatic paths; color-class digraph; quasi color-perfect digraph; color-perfect digraph

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2016
• Tom: 36
• Numer: 2
• Strony: 309-321

Daty

wydano

2016-05-01

otrzymano

2014-08-18

poprawiono

2015-06-23

zaakceptowano

2015-06-23

online

2016-04-15

Twórcy

autor

Hortensia Galeana-Śanchez

• Instituto de Matemáticas UNAM, Ciudad Universitaria Circuito Exterior 04510, México, D.F., México

autor

Rocío Sánchez-López

• Instituto de Matemáticas UNAM, Ciudad Universitaria Circuito Exterior 04510, México, D.F., México

Identyfikatory

DOI

10.7151/dmgt.1860