Induced subgraphs of graphs with large chromatic number. XI. Orientations

Author: 

Chudnovsky, M
Scott, A
Seymour, P

Publication Date: 

1 February 2019

Journal: 

European Journal of Combinatorics

Last Updated: 

2019-04-23T19:23:18.8+01:00

Volume: 

76

DOI: 

10.1016/j.ejc.2018.09.003

page: 

53-61

abstract: 

© 2018 Elsevier Ltd Fix an oriented graph H, and let G be a graph with bounded clique number and very large chromatic number. If we somehow orient its edges, must there be an induced subdigraph isomorphic to H? Kierstead and Rödl (1996) raised this question for two specific kinds of digraph H: the three-edge path, with the first and last edges both directed towards the interior; and stars (with many edges directed out and many directed in). Aboulker et al. (2018) subsequently conjectured that the answer is affirmative in both cases. We give affirmative answers to both questions.

Symplectic id: 

912069

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article