Large Subgraphs without Short Cycles

  title={Large Subgraphs without Short Cycles},
  author={Florent Foucaud and Michael Krivelevich and Guillem Perarnau},
  journal={SIAM J. Discrete Math.},
We study two extremal problems about subgraphs excluding a family F of graphs: (i) Among all graphs with m edges, what is the smallest size f(m,F) of a largest F-free subgraph? (ii) Among all graphs with minimum degree δ and maximum degree Δ, what is the smallest minimum degree h(δ,Δ,F) of a spanning F-free subgraph with largest minimum degree? These questions are easy to answer for families not containing any bipartite graph. We study the case where F is composed of all even cycles of length… CONTINUE READING

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