Bounds for the chromatic number of graphs with partial information

  • Authors:

  • William C. Coffman;S. Louis Hakimi;Edward Schmeichel

  • Affiliations:

  • Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Electrical and Computer Engineering, University of California, Davis, CA;Department of Mathematics, San Jose State University, San Jose, CA

  • Venue:
  • Discrete Mathematics
  • Year:
  • 2003

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Abstract

We obtain bounds for the chromatic and clique numbers of a simple graph, first in terms of the number of vertices and edges it contains, and then in terms of its vertex degrees. In every case, we examine the tightness of the bounds we obtain. We also briefly discuss lower bounds for the independence number of a graph in terms of the same parameters.