Polynomial bounds for chromatic number II: Excluding a star-forest
Abstract
The Gyárfás–Sumner conjecture says that for every forest H, there is a function fH such that if G
is H-free then x(G) ≤ fH(w(G)) (where x,w are the chromatic number and the clique number of
G). Louis Esperet conjectured that, whenever such a statement holds, fH can be chosen to be a
polynomial. The Gyárfás–Sumner conjecture is only known to be true for a modest set of forests H,
and Esperet's conjecture is known to be true for almost no forests. For instance, it is not known
when H is a five-vertex path. Here we prove Esperet's conjecture when each component of H is a
star.
Collections
Cite this version of the work
Alex Scott, Paul Seymour, Sophie Spirkl
(2022).
Polynomial bounds for chromatic number II: Excluding a star-forest. UWSpace.
http://hdl.handle.net/10012/18535
Other formats
The following license files are associated with this item: