Even and odd holes in cap-free graphs

  title={Even and odd holes in cap-free graphs},
  author={Michele Conforti and G{\'e}rard Cornu{\'e}jols and Ajai Kapoor and Kristina Vuskovic},
  journal={J. Graph Theory},
It is an old problem in graph theory to test whether a graph contains a chordless cycle of length greater than three (hole) with a specific parity (even, odd). Studying the structure of graphs without odd holes has obvious implications for Berge's strong perfect graph conjecture that states that a graph G is perfect if and only if neither G nor its complement contain an odd hole. Markossian, Gasparian, and Reed have proven that if neither G nor its complement contain an even hole, then G is… 

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