Dvo\v{r}\'ak and Kawarabayashi [European Journal of Combinatorics, 2017]
asked, what is the largest chromatic number attainable by a graph of treewidth
t with no Krβ subgraph? In this paper, we consider the fractional version
of this question. We prove that if G has treewidth t and clique number 2β€Οβ€t, then Οfβ(G)β€t+tΟβ1β, and we
show that this bound is tight for Ο=t. We also show that for each
value 0<c<21β, there exists a graph G of a large treewidth t
and clique number Ο=β(1βc)tβ satisfying Οfβ(G)β₯t+1+log(1β2c)+o(1).Comment: 9 page