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Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree

  • G. PERARNAU (a1) and B. REED (a2)

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.

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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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