Maximum spread of K_s,t - Minor-free Graphs

Author(s)

• William Linz
• Linyuan Li, University of South CarolinaFollow
• Zhiyu Wang

Document Type

Article

Abstract

The spread of a graph G is the difference between the largest and smallest eigenvalue of the adjacency matrix of G. In this paper, we consider the family of graphs which contain no K_s,t-minor. We show that for any t ≥ s ≥ 2 and sufficiently large n, there is an integer ξ_t such that the extremal n-vertex K_s,t-minor-free graph attaining the maximum spread is the graph obtained by joining a graph L on (s − 1) vertices to the disjoint union of ⌊(2n + ξ_t)/(3t)⌋ copies of K_t and n − s + 1 − t⌊(2n + ξ_t)/(3t)⌋ isolated vertices. Furthermore, we give an explicit formula for ξ_t and an explicit description for the graph L for t ≥ (3/2)(s − 3) + 4/(s − 1).

Digital Object Identifier (DOI)

https://doi.org/10.37236/13410

Publication Info

Published in The Electronic Journal of Combinatorics, Volume 32, Issue 1, 2025.

APA Citation

Linz, W., Lu, L., & Wang, Z. (2025). Maximum spread of $K_{S,T}$-minor-free graphs. The Electronic Journal of Combinatorics, 32(1). a href="https://doi.org/10.37236/13410">https://doi.org/10.37236/13410

Rights

©The authors. Released under the CC BY-ND license (International 4.0).