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MFCS

2005

Springer

2005

Springer

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 ...

Related Content

Added |
28 Jun 2010 |

Updated |
28 Jun 2010 |

Type |
Conference |

Year |
2005 |

Where |
MFCS |

Authors |
Julia Böttcher |

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