Professor Daniel Paulusma daniel.paulusma@durham.ac.uk
Professor
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 -free graphs, that is, graphs with no induced subgraph isomorphic to . 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.
Paulusma, D., Picouleau, C., & Ries, B. (2019). Critical vertices and edges in H-free graphs. Discrete Applied Mathematics, 257, 361-367. https://doi.org/10.1016/j.dam.2018.08.016
Journal Article Type | Article |
---|---|
Acceptance Date | Aug 28, 2018 |
Online Publication Date | Oct 11, 2018 |
Publication Date | Mar 31, 2019 |
Deposit Date | Sep 19, 2018 |
Publicly Available Date | Oct 11, 2019 |
Journal | Discrete Applied Mathematics |
Print ISSN | 0166-218X |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 257 |
Pages | 361-367 |
DOI | https://doi.org/10.1016/j.dam.2018.08.016 |
Public URL | https://durham-repository.worktribe.com/output/1314370 |
Accepted Journal Article
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http://creativecommons.org/licenses/by-nc-nd/4.0/
Copyright Statement
© 2018 This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
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