Coloring Graphs with Sparse Neighborhood
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Noga Alon; Michael Krivelevich; Benny Sudakov
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Article
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1999
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Elsevier Science
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English
โ 118 KB
It is shown that the chromatic number of any graph with maximum degree d in which the number of edges in the induced subgraph on the set of all neighbors of any vertex does not exceed d 2 รf is at most O(dรlog f ). This is tight (up to a constant factor) for all admissible values of d and f.