Polynomial bounds for chromatic number. III. Excluding a double star
Abstract
A double star is a tree with two internal vertices. It is known that the GyárfásSumner conjecture holds for double stars, that is, for every double star $H$, there is a function $f$ such that if $G$ does not contain $H$ as an induced subgraph then $\chi(G)\le f(\omega(G))$ (where $\chi, \omega$ are the chromatic number and the clique number of $G$). Here we prove that $f$ can be chosen to be a polynomial.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.07066
 Bibcode:
 2021arXiv210807066S
 Keywords:

 Mathematics  Combinatorics