Interval minors of complete multipartite graphs

TL;DR

This paper explores the maximum number of edges in interval minor free complete multipartite graphs, extending previous bipartite cases to more general multipartite structures.

Contribution

It generalizes the study of maximum edges in interval minor free graphs from bipartite to multipartite graphs for arbitrary parameters.

Findings

Derived bounds for maximum edges in $K_{k,\, ext{ell}}$-interval minor free bipartite graphs.

Extended analysis to $K_{ ext{ell}_1, ext{ell}_2,\, ext{ell}_t}$-interval minor free multipartite graphs.

Provided new theoretical results on the structure of such graphs.

Abstract

Interval minors of bipartite graphs were introduced by Jacob Fox in the study of Stanley-Wilf limits. Recently, Mohar, Rafiey, Tayfeh-Rezaie and Wu investigated the maximum number of edges in $K_{k,\ell}$-interval minor free bipartite graphs when $k=2$ and $k=3$. In this paper, we investigate the maximum number of edges in $K_{k,\ell}$-interval minor free bipartite graphs for general $k$ and $\ell$. We also study the maximum number of edges in $K_{\ell_1,\ell_2,\cdots,\ell_t}$-interval minor free multipartite graphs.