Odd Hadwiger number and graph products
arXiv:2603.28748
Abstract
The Odd Hadwiger number of a graph is the largest integer such that has a clique of size 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.
Major review. New proof of Theorem 1.1, through the new Theorem 1.2. Also new result for direct product, Theorem 1.6. 11 pages, 4 figures, 2 tables