NDLI: Finding the chromatic number by means of critical graphs

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Finding the chromatic number by means of critical graphs

Content Provider	ACM Digital Library
Author	Herrmann, Francine Hertz, Alain
Copyright Year	2002
Abstract	We propose a new exact algorithm for finding the chromatic number of a graph $\textit{G}.$ The algorithm attempts to determine the smallest possible induced subgraph $\textit{G'}$ of $\textit{G}$ which has the same chromatic number as $\textit{G}.$ Such a subgraph is said critical since all proper induced sub-graph of $\textit{G'}$ have a chromatic number strictly smaller than $\textit{G'}.The$ proposed method is particularly helpful when a $\textit{k}-coloring$ of a non-critical graph is known, and it has to be proved that no $(\textit{k}-1)-coloring$ of $\textit{G}$ exists. Computational experiments on random graphs and on DIMACS benchmark problems demonstate that the new proposed algorithm can solve larger problem than previous known exact methods.
Starting Page	10
File Format	PDF
ISSN	10846654
e-ISSN	10846654
DOI	10.1145/944618.944628
Journal	Journal of Experimental Algorithmics (JEA)
Volume Number	7
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2002-12-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Algorithms Experimentation Performance
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science

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