On graphs all of whose {C₃,T₃}-free arc colorations are kernel-perfect

Hortensia Galeana-Sánchez, and José de Jesús García-Ruvalcaba. "On graphs all of whose {C₃,T₃}-free arc colorations are kernel-perfect." Discussiones Mathematicae Graph Theory 21.1 (2001): 77-93. <http://eudml.org/doc/270329>.

@article{HortensiaGaleana2001,
abstract = { A digraph D is called a kernel-perfect digraph or KP-digraph when every induced subdigraph of D has a kernel. We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows: V( ζ(D)) = V(D), and A( ζ(D)) = ∪\_\{i\} \{(u,v) with colour i: there exists a monochromatic path of colour i from the vertex u to the vertex v contained in D\}. We will denoted by T₃ and C₃, the transitive tournament of order 3 and the 3-directed-cycle respectively; both of whose arcs are coloured with three different colours. Let G be a simple graph. By an m-orientation-coloration of G we mean an m-coloured digraph which is an asymmetric orientation of G. By the class E we mean the set of all the simple graphs G that for any m-orientation-coloration D without C₃ or T₃, we have that ζ(D) is a KP-digraph. In this paper we prove that if G is a hamiltonian graph of class E, then its complement has at most one nontrivial component, and this component is K₃ or a star. },
author = {Hortensia Galeana-Sánchez, José de Jesús García-Ruvalcaba},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {kernel; kernel-perfect digraph; m-coloured digraph; -coloured digraph},
language = {eng},
number = {1},
pages = {77-93},
title = {On graphs all of whose \{C₃,T₃\}-free arc colorations are kernel-perfect},
url = {http://eudml.org/doc/270329},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Hortensia Galeana-Sánchez
AU - José de Jesús García-Ruvalcaba
TI - On graphs all of whose {C₃,T₃}-free arc colorations are kernel-perfect
JO - Discussiones Mathematicae Graph Theory
PY - 2001
VL - 21
IS - 1
SP - 77
EP - 93
AB - A digraph D is called a kernel-perfect digraph or KP-digraph when every induced subdigraph of D has a kernel. We call the digraph D an m-coloured digraph if the arcs of D are coloured with m distinct colours. A path P is monochromatic in D if all of its arcs are coloured alike in D. The closure of D, denoted by ζ(D), is the m-coloured digraph defined as follows: V( ζ(D)) = V(D), and A( ζ(D)) = ∪_{i} {(u,v) with colour i: there exists a monochromatic path of colour i from the vertex u to the vertex v contained in D}. We will denoted by T₃ and C₃, the transitive tournament of order 3 and the 3-directed-cycle respectively; both of whose arcs are coloured with three different colours. Let G be a simple graph. By an m-orientation-coloration of G we mean an m-coloured digraph which is an asymmetric orientation of G. By the class E we mean the set of all the simple graphs G that for any m-orientation-coloration D without C₃ or T₃, we have that ζ(D) is a KP-digraph. In this paper we prove that if G is a hamiltonian graph of class E, then its complement has at most one nontrivial component, and this component is K₃ or a star.
LA - eng
KW - kernel; kernel-perfect digraph; m-coloured digraph; -coloured digraph
UR - http://eudml.org/doc/270329
ER -