Lower bounds for treewidth of product graphs

Authors:
Kyohei Kozawa;Yota Otachi;Koichi Yamazaki
Affiliations:
-;-;-
Venue:
Discrete Applied Mathematics
Year:
2014

Citing 11
Cited 0

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Abstract

Two lower bounds for the treewidth of product graphs are presented in terms of the bramble number. The first bound is that the bramble number of the Cartesian product of graphs G"1 and G"2 must be at least the product of the Hadwiger number of G"1 and the PI number of G"2, where the PI number is a new graph parameter introduced in this paper. The second bound is that the bramble number of the strong product of graphs G"1 and G"2 must be at least the product of the Hadwiger number of G"1 and the bramble number of G"2. We also demonstrate applications of the lower bounds.