A bound on the treewidth of planar even-hole-free graphs

The class of planar graphs has unbounded treewidth, since the k × k grid, ∀ k ∈ N , is planar and has treewidth k . So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if G is an even-hole-free planar graph, then it does not contai...

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Bibliographic Details
Published inDiscrete Applied Mathematics Vol. 158; no. 12; pp. 1229 - 1239
Main Authors Silva, Ana, da Silva, Aline Alves, Sales, Cláudia Linhares
Format Journal Article Conference Proceeding
LanguageEnglish
Published Kidlington Elsevier B.V 28.06.2010
Elsevier
Subjects
Algorithmics. Computability. Computer arithmetics
Applied sciences
Bounded treewidth
Combinatorics
Combinatorics. Ordered structures
Computer Science
Computer science; control theory; systems
Discrete Mathematics
Even-hole-free graphs
Exact sciences and technology
Forbidden minor
Information retrieval. Graph
Mathematics
Planar graphs
Sciences and techniques of general use
Theoretical computing
Bounded treewidth
Forbidden minor
Even-hole-free graphs
Planar graphs
Hole
Grid pattern
Computer theory
Planar graph
Combinatorics
Optimization
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Summary:The class of planar graphs has unbounded treewidth, since the k × k grid, ∀ k ∈ N , is planar and has treewidth k . So, it is of interest to determine subclasses of planar graphs which have bounded treewidth. In this paper, we show that if G is an even-hole-free planar graph, then it does not contain a 9×9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2009.07.010