Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree. (7th December 2016) - PERARNAU, G.; REED, B.
Abstract : Let ℱ be a family of graphs and let d be large enough. For every d -regular graph G, we study the existence of a spanning ℱ-free subgraph of G with large minimum degree. This problem is well understood if ℱ does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs. To prove these results, we study a locally injective analogue of the question.