Random I‐colorable graphs

Authors:
Hans Jürgen Prömel;Angelika Steger
Affiliations:
Institut für Informatik, Humbold‐Universität zu Berlin, Unter den Linden 6, 10099 Berlin;Institut für Informatik, Humbold‐Universität zu Berlin, Unter den Linden 6, 10099 Berlin
Venue:
Random Structures & Algorithms
Year:
1995

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ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation

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Abstract

In this article we investigate properties of the class of all l‐colorable graphs on n vertices, where l = l(n) may depend on n. Let Gln denote a uniformly chosen element of this class, i.e., a random l‐colorable graph. For a random graph Gln we study in particular the property of being uniquely l‐colorable. We show that not only does there exist a threshold function l = l(n) for this property, but this threshold corresponds to the chromatic number of a random graph. We also prove similar results for the class of all l‐colorable graphs on n vertices with m = m(n) edges. © 1995 Wiley Periodicals, Inc.