# 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} }

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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