Odd Hadwiger number and graph products
Henry Echeverr\'ia, Andrea Jim\'enez, Suchismita Mishra, Daniel A. Quiroz, Mauricio Y\'epez
TL;DR
This paper explores the Odd Hadwiger number in graph theory, specifically analyzing how large it can be for various graph products, and provides optimal bounds for certain cases.
Contribution
It offers new bounds on the Odd Hadwiger number for the product of two graphs, with optimal results for strong and lexicographic products.
Findings
Established lower bounds for the Odd Hadwiger number in graph products.
Provided optimal bounds for strong and lexicographic graph products.
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.
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