### Rutgers Discrete Mathematics Seminar

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

Speaker: **Sophie Spirkl**, Princeton University

Date: Monday, October 23, 2017 2:00 pm

Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ

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.

See: http://sites.math.rutgers.edu/~ajr224/DM