Odd Hadwiger number and graph products
Combinatorics
2026-03-31 v1
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.
Cite
@article{arxiv.2603.28748,
title = {Odd Hadwiger number and graph products},
author = {Henry Echeverría and Andrea Jiménez and Suchismita Mishra and Daniel A. Quiroz and Mauricio Yépez},
journal= {arXiv preprint arXiv:2603.28748},
year = {2026}
}
Comments
12 pages, 6 figures, 2 tables