Computing the Tutte Polynomial on Graphs of Bounded Clique-Width

The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded tree-width. The notion of clique-width extends the definition of cograhs (graphs without induced P4), and it is a more general notion...

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Bibliographic Details
Published inGraph-Theoretic Concepts in Computer Science pp. 59 - 68
Main Authors Giménez, Omer, Hliněný, Petr, Noy, Marc
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
SeriesLecture Notes in Computer Science
Subjects
clique-width
cographs
polynomial
subexponential algorithm
Tutte polynomial
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Summary:The Tutte polynomial is a notoriously hard graph invariant, and efficient algorithms for it are known only for a few special graph classes, like for those of bounded tree-width. The notion of clique-width extends the definition of cograhs (graphs without induced P4), and it is a more general notion than that of tree-width. We show a subexponential algorithm (running in time expO(n2/3)) for computing the Tutte polynomial on cographs. The algorithm can be extended to a subexponential algorithm computing the Tutte polynomial on on all graphs of bounded clique-width. In fact, our algorithm computes the more general U-polynomial. 2000 Math Subjects Classification: 05C85, 68R10.
ISBN:3540310002
9783540310006
ISSN:0302-9743
1611-3349
DOI:10.1007/11604686_6