Faculty Publications & Research
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 Ks,t for a fixed s and large t. Myers proved upper bounds on D(Ks,t ) and made a conjecture on the order of magnitude of D(Ks,t ) for a fixed s and t → ∞. He also found exact values for D(K2,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(Ks,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.