Dense Induced Subgraphs of Dense Bipartite Graphs

@article{McCarty2021DenseIS,
  title={Dense Induced Subgraphs of Dense Bipartite Graphs},
  author={Rose McCarty},
  journal={SIAM J. Discret. Math.},
  year={2021},
  volume={35},
  pages={661-667}
}
  • Rose McCarty
  • Published 31 March 2020
  • Mathematics
  • SIAM J. Discret. Math.
We prove that every bipartite graph of sufficiently large average degree has either a $K_{t,t}$-subgraph or an induced subgraph of average degree at least $t$ and girth at least $6$. We conjecture that "$6$" can be replaced by "$k$", which strengthens a conjecture of Thomassen. In support of this conjecture, we show that it holds for regular graphs. 
C4-free subgraphs with large average degree
Motivated by a longstanding conjecture of Thomassen, we study how large the average degree of a graph needs to be to imply that it contains a $C_4$-free subgraph with average degree at least $t$.

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