Strong branchwidth and local transversals

Authors:
Zsolt Tuza
Affiliations:
Computer and Automation Institute, Hungarian Academy of Sciences, Kende u. 13-17, Budapest H-1111, Hungary and Department of Computer Science, University of Veszprém, Hungary
Venue:
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Year:
2005

Citing 4
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Journal of Combinatorial Theory Series B
Graph classes: a survey

Graph classes: a survey
Graphs with branchwidth at most three

Journal of Algorithms
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)

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Abstract

We consider representations of chordal graphs as edge intersection graphs of subtrees in a tree of maximum vertex degree 3. A new graph invariant related to the concept of branchwidth is introduced, and a structural characterization theorem is given for the existence of representations where each edge is contained in fewer subtrees than the clique number of the graph represented. As a consequence, a sufficient condition is obtained for chordal graphs to have smaller branchwidth than clique number.