Consecutive holes

@inproceedings{Scott2015ConsecutiveH,
  title={Consecutive holes},
  author={Alexander Scott and Paul Seymour},
  year={2015}
}
A hole in a graph is an induced subgraph which is a cycle of length at least four. We prove that for all ν > 0, every triangle-free graph with sufficiently large chromatic number contains holes of ν consecutive lengths. In particular, this implies two well-known conjectures of Gyárfás [3], namely that every triangle-free graph with sufficiently large chromatic number has a hole of length at least k, and every such graph has an odd hole of length at least k. It was not known until now that every… CONTINUE READING

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Problems from the world surrounding perfect graphs

  • A. Gyárfás
  • Proceedings of the International Conference on…
  • 1987
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