On the structure of (banner, odd hole)‐free graphs

@article{Hong2018OnTS,
  title={On the structure of (banner, odd hole)‐free graphs},
  author={Ch{\'i}nh T. Ho{\`a}ng},
  journal={Journal of Graph Theory},
  year={2018},
  volume={89},
  pages={395 - 412}
}
  • C. Hoàng
  • Published 8 October 2015
  • Mathematics
  • Journal of Graph Theory
A hole is a chordless cycle with at least four vertices. A hole is odd if it has an odd number of vertices. A banner is a graph that consists of a hole on four vertices and a single vertex with precisely one neighbor on the hole. We prove that a (banner, odd hole)‐free graph is perfect, or does not contain a stable set on three vertices, or contains a homogeneous set. Using this structure result, we design a polynomial‐time algorithm for recognizing (banner, odd hole)‐free graphs. We also… 
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