# Seminars & Colloquia Calendar

## Gyarfas-Sumner meets Erdos-Hajnal

#### Paul Seymour, Princeton

Location: ** Hill 705**

Date & time: Monday, 19 February 2018 at 2:00PM - 3:00PM

**Abstract:**

The Gyarfas-Sumner conjecture says that every graph with huge (enough) chromatic number and bounded clique number contains any given forest as an induced subgraph. The Erdos-Hajnal conjecture says that for every graph H, all graphs not containing H as an induced subgraph have a clique or stable set of polynomial size.

This talk is about a third problem related to both of these, the following.Say an n-vertex graph is "c-coherent'' if every vertex has degree <cn, and every two disjoint vertex subsets of size at least cn have an edge between them. To prove a given graph H satisfies the Erdos-Hajnal conjecture, it is enough to prove H satisfies the conjecture in all c-coherent graphs and their complements, where c>0 is fixed and as small as we like. But for some graphs H, all c-coherent graphs contain H if c is small enough, so half of the task is done for free.Which graphs H have this property? Paths do (a theorem of Bousquet, Lagoutte, and Thomasse), and non-forests don't. Maybe all forests do? In other words, do all c-coherent graphs with c small enough contain any given forest as an induced subgraph?

That question is the topic of the talk. It looks much like the Gyarfas-Sumner conjecture, but it seems easier, and there are already several pretty results. For instance the conjecture is true for all subdivided caterpillars (which is more than we know for Gyarfas-Sumner), and all trees of radius two.

Joint work with Maria Chudnovsky, Anita Liebenau, Marcin Pilipczuk, Alex Scott and Sophie Spirkl.

Chiara Damiolini, Ian Coley and Franco Rota -Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

P. Gupta, X.Huang and J. Song Organizer's webpage

Swastik Kopparty, Sepehr Assadi Seminar webpage

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Brooke Ogrodnik, Website

Robert Dougherty-Bliss and Doron Zeilberger --> homepage

Paul Feehan, Daniel Ketover, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Jason Saied Seminar webpage

Brian Pinsky, Rashmika Goswami website

Quentin Dubroff Organizer's webpage

James Holland; Organizer website

Edna Jones Organizer's webpage

Brooke Ogrodnik website

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum Organizer's Webpage

Organizer: Luochen Zhao

Yanyan Li, Zheng-Chao Han, Natasa Sesum, Jian Song Organizer's Page

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's webpage

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis Organizer's Webpage

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Alex Walker seminar website

Stephen D. Miller

Brooke Ogrodnik, Website

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Yael Davidov Seminar webpage

Kristen Hendricks, Xiaochun Rong, Hongbin Sun, Chenxi Wu Organizer's page

Fioralba Cakoni Seminar webpage

Ebru Toprak, Organizer

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