DIMACS TR: 98-32

Coloring Graphs with Sparse Neighborhoods

Authors: Noga Alon, Michael Krivelevich and Benny Sudakov


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/f is at most O( d/ \log f). This is tight (up to a constant factor) for all admissible values of d and f.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1998/98-32.ps.gz
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