Induced subgraphs of graphs with large chromatic number. XII. Distant stars

Author: 

Chudnovsky, M
Scott, A
Seymour, P

Publication Date: 

November 2019

Journal: 

JOURNAL OF GRAPH THEORY

Last Updated: 

2019-11-01T03:12:43.903+00:00

Issue: 

3

Volume: 

92

DOI: 

10.1002/jgt.22450

page: 

237-254

abstract: 

© 2019 Wiley Periodicals, Inc. The Gyárfás-Sumner conjecture asserts that if H is a tree then every graph with bounded clique number and very large chromatic number contains H as an induced subgraph. This is still open, although it has been proved for a few simple families of trees, including trees of radius two, some special trees of radius three, and subdivided stars. These trees all have the property that their vertices of degree more than two are clustered quite closely together. In this paper, we prove the conjecture for two families of trees which do not have this restriction. As special cases, these families contain all double-ended brooms and two-legged caterpillars.

Symplectic id: 

953280

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article