From Tree-Width to Clique-Width: Excluding a Unit Interval Graph
- Cite this paper as:
- Lozin V.V. (2008) From Tree-Width to Clique-Width: Excluding a Unit Interval Graph. In: Hong SH., Nagamochi H., Fukunaga T. (eds) Algorithms and Computation. ISAAC 2008. Lecture Notes in Computer Science, vol 5369. Springer, Berlin, Heidelberg
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.
KeywordsTree-width Clique-width Unit interval graphs Fixed parameter tractability
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