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2005
Springer

Coloring Sparse Random k-Colorable Graphs in Polynomial Expected Time

12 years 3 months ago
Coloring Sparse Random k-Colorable Graphs in Polynomial Expected Time
Abstract. Feige and Kilian [5] showed that finding reasonable approximative solutions to the coloring problem on graphs is hard. This motivates the quest for algorithms that either solve the problem in most but not all cases, but are of polynomial time complexity, or that give a correct solution on all input graphs while guaranteeing a polynomial running time on average only. An algorithm of the first kind was suggested by Alon and Kahale in [1] for the following type of random k-colorable graphs: Construct a graph Gn,p,k on vertex set V of cardinality n by first partitioning V into k equally sized sets and then adding each edge between these sets with probability p independently from each other. Alon and Kahale showed that graphs from Gn,p,k can be k-colored in polynomial time with high probability as long as p ≥ c/n for some sufficiently large constant c. In this paper, we construct an algorithm with polynomial expected running time for k = 3 on the same type of graphs and for ...
Julia Böttcher
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where MFCS
Authors Julia Böttcher
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