From: utzoo!watmath!mwang Newsgroups: ont.events Title: UW Theory Seminar, Dr. Aspvall on "Graph Coloring Using Eigenvalue Decomposition" Article-I.D.: watmath.4837 Posted: Tue Apr 5 10:33:07 1983 Received: Tue Apr 5 23:39:18 1983 Expires: Fri Apr 15 00:00:00 1983 DEPARTMENT OF COMPUTER SCIENCE UNIVERSITY OF WATERLOO SEMINAR ACTIVITIES THEORY SEMINAR - Thursday, April 14, 1983. Dr. B. Aspvall of Cornell University will speak on ``Graph Coloring Using Eigenvalue Decomposition''. TIME: 3.30 PM ROOM: MC 5158 ABSTRACT Determining whether the vertices of a graph can be colored using $ ~ k ~$ different colors so that no two adjacent vertices receive the same color is a well- known NP-complete problem. Graph coloring is also of practical interest (for example, in estimating sparse Jacobians and in scheduling), and many heuristic algo- rithms have been developed. We present a heuristic algorithm based on the eigenvalue decomposition of the adjacency matrix of a graph. Eigenvectors point out ``bipartite-looking'' subgraphs that are used to refine the coloring to a valid coloring. The algorithm optimally colors complete $ k $-partite graphs and cer- tain other classes of graphs with regular structure. Using perturbation arguments, we argue that the algo- rithm colors a wide range of graphs well. April 5, 1983