Kernels by Monochromatic Paths and Color-Perfect Digraphs

Hortensia Galeana-Śanchez, and Rocío Sánchez-López. "Kernels by Monochromatic Paths and Color-Perfect Digraphs." Discussiones Mathematicae Graph Theory 36.2 (2016): 309-321. <http://eudml.org/doc/277132>.

@article{HortensiaGaleana2016,
abstract = {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.},
author = {Hortensia Galeana-Śanchez, Rocío Sánchez-López},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {kernel; kernel perfect digraph; kernel by monochromatic paths; color-class digraph; quasi color-perfect digraph; color-perfect digraph},
language = {eng},
number = {2},
pages = {309-321},
title = {Kernels by Monochromatic Paths and Color-Perfect Digraphs},
url = {http://eudml.org/doc/277132},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Hortensia Galeana-Śanchez
AU - Rocío Sánchez-López
TI - Kernels by Monochromatic Paths and Color-Perfect Digraphs
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 2
SP - 309
EP - 321
AB - 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.
LA - eng
KW - kernel; kernel perfect digraph; kernel by monochromatic paths; color-class digraph; quasi color-perfect digraph; color-perfect digraph
UR - http://eudml.org/doc/277132
ER -