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Erschienen in:
2009 | OriginalPaper | Buchkapitel
A Complete Characterisation of the Linear Clique-Width of Path Powers
verfasst von : Pinar Heggernes, Daniel Meister, Charis Papadopoulos
Erschienen in: Theory and Applications of Models of Computation
Verlag: Springer Berlin Heidelberg
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A
k
-path power is the
k
-power graph of a simple path of arbitrary length. Path powers form a non-trivial subclass of proper interval graphs. Their clique-width is not bounded by a constant, and no polynomial-time algorithm is known for computing their clique-width or linear clique-width. We show that
k
-path powers above a certain size have linear clique-width exactly
k
+ 2, providing the first complete characterisation of the linear clique-width of a graph class of unbounded clique-width. Our characterisation results in a simple linear-time algorithm for computing the linear clique-width of all path powers.