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Discrete Math

The structure of triangle-free graphs with no induced six-vertex path

Sophie Spirkl, Princeton

Location:  HILL 705
Date & time: Monday, 23 October 2017 at 2:00PM - 3:00PM

Abstract:  I will talk about an explicit construction for triangle-free graphs that do not contain a six-vertex path as an induced subgraph. Examples include the 16-vertex Clebsch graph, and the graph that arises from a complete bipartite graph by subdividing every edge of a perfect matching exactly once. We show that every connected triangle-free graph with no six-vertex induced path can be obtained from an induced subgraph of one of these two by restricted homogeneous set and homogeneous pair operations.

Joint work with Maria Chudnovsky, Paul Seymour, and Mingxian Zhong.

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