Chapter

Graph-Theoretic Concepts in Computer Science

Volume 4271 of the series Lecture Notes in Computer Science pp 191-204

Computing Graph Polynomials on Graphs of Bounded Clique-Width

  • J. A. MakowskyAffiliated withDepartment of Computer Science, Technion–Israel Institute of Technology
  • , Udi RoticsAffiliated withSchool of Computer Science and Mathematics, Netanya Academic College
  • , Ilya AverbouchAffiliated withDepartment of Computer Science, Technion–Israel Institute of Technology
  • , Benny GodlinAffiliated withDepartment of Computer Science, Technion–Israel Institute of TechnologyIBM Research and Development Laboratory

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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(n f( k)), where f(k) ≤3 for the inerlace polynomial, f(k) ≤2k+1 for the matching polynomial and f(k) ≤3 https://static-content.springer.com/image/chp%3A10.1007%2F11917496_18/MediaObjects/978-3-540-48382-3_18_IEq1_HTML.png 2 k + 2 for the chromatic polynomial.