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

Authors:
Ana Silva;Aline Alves da Silva;Cláudia Linhares Sales
Affiliations:
Laboratoire G-SCOP, Université Joseph Fourier (Grenoble I), 46 av. Félix Viallet 38000 Grenoble, France;Departamento de Computação - UFC, Campus do Pici, bloco 910, CEP 60455-760, Fortaleza, Brazil;Departamento de Computação - UFC, Campus do Pici, bloco 910, CEP 60455-760, Fortaleza, Brazil
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

The class of planar graphs has unbounded treewidth, since the kxk 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 9x9 grid minor. As a result, we have that even-hole-free planar graphs have treewidth at most 49.