Affiliation:
1. School of Mathematical Sciences University of Science and Technology of China Hefei China
2. Hefei National Laboratory University of Science and Technology of China Hefei China
3. Shanghai Center for Mathematical Sciences Fudan University Shanghai China
Abstract
AbstractWe prove that there exists an absolute constant such that, for any positive integer , every graph with minimum degree at least admits a vertex‐partition , where both and have minimum degree at least , and every vertex in has at least neighbors in . This confirms a question posted by Kühn and Osthus (J. Comb. Theory Ser. B. 88 (2003), 29–43.) and is tight up to a constant factor. Our proof combines probabilistic methods with structural arguments based on Ore's theorem on ‐factors of bipartite graphs.
Funder
National Key Research and Development Program of China
National Natural Science Foundation of China