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ICALP

2011

Springer

2011

Springer

In [13], Erd˝os et al. deﬁned the local chromatic number of a graph as the minimum number of colors that must appear within distance 1 of a vertex. For any ∆ ≥ 2, there are graphs with arbitrarily large chromatic number that can be colored so that (i) no vertex neighborhood contains more than ∆ diﬀerent colors (bounded local colorability), and (ii) adjacent vertices from two color classes induce a complete bipartite graph (biclique coloring). We investigate the weighted vertex cover problem in graphs when a locally bounded coloring is given. This generalizes the vertex cover problem in bounded degree graphs to a class of graphs with arbitrarily large chromatic number. Assuming the Unique Game Conjecture, we provide a tight characterization. We prove that it is UGC-hard to improve the approximation ratio of 2 − 2/(∆ + 1) if the given local coloring is not a biclique coloring. A matching upper bound is also provided. Vice versa, when properties (i) and (ii) hold, we presen...

Related Content

Added |
29 Aug 2011 |

Updated |
29 Aug 2011 |

Type |
Journal |

Year |
2011 |

Where |
ICALP |

Authors |
Fabian Kuhn, Monaldo Mastrolilli |

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