Year: 2011
Type: article
Abstract: Given a bipartite graph H and a positive integer n such that v ( H ) divides 2 n , we define the minimum degree threshold for bipartite H ‐tiling, δ 2 ( n, H ), as the smallest integer k such that every bipartite graph G with n vertices in each partition and minimum degree δ( G )≥ k contains a spanning subgraph consisting of vertex‐disjoint copies of H . Zhao, Hladký‐Schacht, Czygrinow‐DeBiasio determined δ 2 ( n, K s, t ) exactly for all s ⩽ t and suffi‐ciently large n . In this article we determine δ 2 ( n, H ), up to an additive constant, for all bipartite H and sufficiently large n . Additionally, we give a corresponding minimum degree threshold to guarantee that G has an H ‐tiling missing only a constant number of vertices. Our δ 2 ( n, H ) depends on either the chromatic number χ( H ) or the critical chromatic number χ cr ( H ), while the threshold for the almost perfect tiling only depends on χ cr ( H ). These results can be viewed as bipartite analogs to the results of Kuhn and Osthus [Combinatorica 29 (2009), 65–107] and of Shokoufandeh and Zhao [Rand Struc Alg 23 (2003), 180–205]. © 2011 Wiley Periodicals, Inc. J Graph Theory
Source: Journal of Graph Theory
DOI: 10.1002/jgt.20605
Authors: Albert Bush, Yi Zhao
Institution: Georgia State University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2159692360