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Critical vertices and edges in H-free graphs

Paulusma, Daniël; Picouleau, Christophe; Ries, Bernard (2019), Critical vertices and edges in H-free graphs, Discrete Applied Mathematics, 257, p. 361-367. 10.1016/j.dam.2018.08.016

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Type
Article accepté pour publication ou publié
Date
2019
Journal name
Discrete Applied Mathematics
Volume
257
Publisher
Elsevier
Pages
361-367
Publication identifier
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Author(s)
Paulusma, Daniël

Picouleau, Christophe cc

Ries, Bernard
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
A vertex or edge in a graph is critical if its deletion reduces the chromatic number of the graph by one. We consider the problems of deciding whether a graph has a critical vertex or edge, respectively. We give a complexity dichotomy for both problems restricted to H-free graphs, that is, graphs with no induced subgraph isomorphic to H. Moreover, we show that an edge is critical if and only if its contraction reduces the chromatic number by one. Hence, we also obtain a complexity dichotomy for the problem of deciding if a graph has an edge whose contraction reduces the chromatic number by one.
Subjects / Keywords
vertex deletion; edge contraction; chromatic number