### Finding the chromatic number by means of critical graphsFinding the chromatic number by means of critical graphs

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 Author Herrmann, Francine ♦ Hertz, Alain Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2002 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Computer programming, programs & data Subject Keyword Algorithms ♦ Experimentation ♦ Performance 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. ISSN 10846654 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2002-12-01 Publisher Place New York e-ISSN 10846654 Journal Journal of Experimental Algorithmics (JEA) Volume Number 7 Starting Page 10

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Source: ACM Digital Library