# Kernels in monochromatic path digraphs

Hortensia Galeana-Sánchez; Laura Pastrana Ramírez; Hugo Alberto Rincón Mejía

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 3, page 407-417
- ISSN: 2083-5892

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topHortensia Galeana-Sánchez, Laura Pastrana Ramírez, and Hugo Alberto Rincón Mejía. "Kernels in monochromatic path digraphs." Discussiones Mathematicae Graph Theory 25.3 (2005): 407-417. <http://eudml.org/doc/270464>.

@article{HortensiaGaleana2005,

abstract = {
We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. Let D be an m-coloured digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions:
(i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and
(ii) for each vertex x ∈ (V(D)-N) there is a vertex y ∈ N such that there is an xy-monochromatic directed path.
In this paper is defined the monochromatic path digraph of D, MP(D), and the inner m-colouration of MP(D). Also it is proved that if D is an m-coloured digraph without monochromatic directed cycles, then the number of kernels by monochromatic paths in D is equal to the number of kernels by monochromatic paths in the inner m-colouration of MP(D). A previous result is generalized.
},

author = {Hortensia Galeana-Sánchez, Laura Pastrana Ramírez, Hugo Alberto Rincón Mejía},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {kernel; line digraph; kernel by monochromatic paths; monochromatic path digraph; edge-coloured digraph; line graph; edge-colored digraph},

language = {eng},

number = {3},

pages = {407-417},

title = {Kernels in monochromatic path digraphs},

url = {http://eudml.org/doc/270464},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Hortensia Galeana-Sánchez

AU - Laura Pastrana Ramírez

AU - Hugo Alberto Rincón Mejía

TI - Kernels in monochromatic path digraphs

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 3

SP - 407

EP - 417

AB -
We call the digraph D an m-coloured digraph if its arcs are coloured with m colours. A directed path (or a directed cycle) is called monochromatic if all of its arcs are coloured alike. Let D be an m-coloured digraph. A set N ⊆ V(D) is said to be a kernel by monochromatic paths if it satisfies the following two conditions:
(i) for every pair of different vertices u,v ∈ N there is no monochromatic directed path between them and
(ii) for each vertex x ∈ (V(D)-N) there is a vertex y ∈ N such that there is an xy-monochromatic directed path.
In this paper is defined the monochromatic path digraph of D, MP(D), and the inner m-colouration of MP(D). Also it is proved that if D is an m-coloured digraph without monochromatic directed cycles, then the number of kernels by monochromatic paths in D is equal to the number of kernels by monochromatic paths in the inner m-colouration of MP(D). A previous result is generalized.

LA - eng

KW - kernel; line digraph; kernel by monochromatic paths; monochromatic path digraph; edge-coloured digraph; line graph; edge-colored digraph

UR - http://eudml.org/doc/270464

ER -

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