# Kernels and cycles' subdivisions in arc-colored tournaments

Pietra Delgado-Escalante; Hortensia Galeana-Sánchez

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 1, page 101-117
- ISSN: 2083-5892

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topPietra Delgado-Escalante, and Hortensia Galeana-Sánchez. "Kernels and cycles' subdivisions in arc-colored tournaments." Discussiones Mathematicae Graph Theory 29.1 (2009): 101-117. <http://eudml.org/doc/270273>.

@article{PietraDelgado2009,

abstract = {Let D be a digraph. D is said to be an m-colored digraph if the arcs of D are colored with m colors. A path P in D is called monochromatic if all of its arcs are colored alike. Let D be an m-colored digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths of D if it satisfies the following conditions: a) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them; and b) for every vertex x ∈ V(D)-N there is a vertex n ∈ N such that there is an xn-monochromatic directed path in D. In this paper we prove that if T is an arc-colored tournament which does not contain certain subdivisions of cycles then it possesses a kernel by monochromatic paths. These results generalize a well known sufficient condition for the existence of a kernel by monochromatic paths obtained by Shen Minggang in 1988 and another one obtained by Hahn et al. in 2004. Some open problems are proposed.},

author = {Pietra Delgado-Escalante, Hortensia Galeana-Sánchez},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {kernel; kernel by monochromatic paths; tournament},

language = {eng},

number = {1},

pages = {101-117},

title = {Kernels and cycles' subdivisions in arc-colored tournaments},

url = {http://eudml.org/doc/270273},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Pietra Delgado-Escalante

AU - Hortensia Galeana-Sánchez

TI - Kernels and cycles' subdivisions in arc-colored tournaments

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 1

SP - 101

EP - 117

AB - Let D be a digraph. D is said to be an m-colored digraph if the arcs of D are colored with m colors. A path P in D is called monochromatic if all of its arcs are colored alike. Let D be an m-colored digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths of D if it satisfies the following conditions: a) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them; and b) for every vertex x ∈ V(D)-N there is a vertex n ∈ N such that there is an xn-monochromatic directed path in D. In this paper we prove that if T is an arc-colored tournament which does not contain certain subdivisions of cycles then it possesses a kernel by monochromatic paths. These results generalize a well known sufficient condition for the existence of a kernel by monochromatic paths obtained by Shen Minggang in 1988 and another one obtained by Hahn et al. in 2004. Some open problems are proposed.

LA - eng

KW - kernel; kernel by monochromatic paths; tournament

UR - http://eudml.org/doc/270273

ER -

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