Computing graph polynomials on graphs of bounded clique-width

Authors:
J. A. Makowsky;Udi Rotics;Ilya Averbouch;Benny Godlin
Affiliations:
Department of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel;School of Computer Science and Mathematics, Netanya Academic College, Netanya, Israel;Department of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel;Department of Computer Science, Technion–Israel Institute of Technology, Haifa, Israel
Venue:
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Year:
2006

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Abstract

We discuss the complexity of computing various graph polynomials of graphs of fixed clique-width. We show that the chromatic polynomial, the matching polynomial and the two-variable interlace polynomial of a graph G of clique-width at most k with n vertices can be computed in time O(nf( k)), where f(k) ≤3 for the inerlace polynomial, f(k) ≤2k+1 for the matching polynomial and f(k) ≤3 2k+2 for the chromatic polynomial.