On K_s,t-minors in Graphs with Given Average Degree

Authors

A. V. Kostochka
N. Prince, Illinois Mathematics and Science AcademyFollow

Document Type

Article

Publication Date

2008

Disciplines

Discrete Mathematics and Combinatorics | Mathematics

Abstract

Let D(H) be the minimum d such that every graph G with average degree d has an H-minor. Myers and Thomason found good bounds on D(H) for almost all graphs H and proved that for 'balanced' H random graphs provide extremal examples and determine the extremal function. Examples of 'unbalanced graphs' are complete bipartite graphs K_s,t for a fixed s and large t. Myers proved upper bounds on D(K_s,t ) and made a conjecture on the order of magnitude of D(K_s,t ) for a fixed s and t → ∞. He also found exact values for D(K_2,t) for an infinite series of t. In this paper, we confirm the conjecture of Myers and find asymptotically (in s) exact bounds on D(K_s,t ) for a fixed s and large t.

Recommended Citation

Kostochka, A.V., & Prince, N. (2008). On K_{s,t}-minors in graphs with given average degree. Discrete Mathematics, 308(19), 4435-4445.