Odd Hadwiger number and graph products
Abstract
The Odd Hadwiger number of a graph G is the largest integer r such that G has a clique of size r as an odd minor. In this paper, we investigate how large is the Odd Hadwiger number of the product of two graphs, when considering any of the four standard graph products: Cartesian, direct, lexicographic, strong. We provide an optimal lower bound in the cases of the strong and lexicographic products.
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