Chapter

Algorithms and Computation

Volume 5369 of the series Lecture Notes in Computer Science pp 871-882

From Tree-Width to Clique-Width: Excluding a Unit Interval Graph

  • Vadim V. LozinAffiliated withDIMAP and Mathematics Institute, University of Warwick

* Final gross prices may vary according to local VAT.

Get Access

Abstract

From the theory of graph minors we know that the class of planar graphs is the only critical class with respect to tree-width. In the present paper, we reveal a critical class with respect to clique-width, a notion generalizing tree-width. This class is known in the literature under different names, such as unit interval, proper interval or indifference graphs, and has important applications in various fields, including molecular biology. We prove that the unit interval graphs constitute a minimal hereditary class of unbounded clique-width. As an application, we show that list coloring is fixed parameter tractable in the class of unit interval graphs.

Keywords

Tree-width Clique-width Unit interval graphs Fixed parameter tractability