منابع مشابه
A Note on Bipartite Graph Tiling
Bipartite graph tiling was studied by Zhao [7] who gave the best possible minimum degree conditions for a balanced bipartite graph on 2ms vertices to contain m vertex disjoint copies of Ks,s. Let s < t be fixed positive integers. Hladký and Schacht [3] gave minimum degree conditions for a balanced bipartite graph on 2m(s + t) vertices to contain m vertex disjoint copies of Ks,t. Their results w...
متن کاملBipartite Graph Tiling
For each s ≥ 2, there exists m0 such that the following holds for all m ≥ m0: Let G be a bipartite graph with n = ms vertices in each partition set. If m is odd and minimum degree δ(G) ≥ n+3s 2 − 2, then G contains m vertex-disjoint copies of Ks,s. If m is even, the same holds under the weaker condition δ(G) ≥ n/2+ s− 1. This is sharp and much stronger than a conjecture of Wang [25] (for large n).
متن کاملNote on Bipartite Graph Tilings
Let s < t be two fixed positive integers. We determine sufficient minimum degree conditions for a bipartite graph G, with both color classes of size n = k(s + t), which ensure that G has a Ks,t-factor. Our result extends the work of Zhao, who determined the minimum degree threshold which guarantees that a bipartite graph has a Ks,s-factor.
متن کاملMinimum degree thresholds for bipartite graph tiling
Given a bipartite graph H and a positive integer n such that v(H) divides 2n, we define the minimum degree threshold for bipartite H-tiling, δ2(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...
متن کاملMinimum degree threshold for bipartite graph tiling
We answer a question of Zhao [SIAM J. Disc. Math. 23 vol.2, (2009), 888-900] that determines the minimum degree threshold for a bipartite graph G to contain an H-factor (a perfect tiling of G with H) for any bipartite graph H. We also show that this threshold is best possible up to a constant depending only on H. This result can be viewed as an analog to Kuhn and Osthus' result [Combinatorica 2...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100788203