Removing logarithmic factors for bounded treewidth and cliquewidth

Determine whether every hypergraph of balls in a graph of treewidth at most t (respectively, cliquewidth at most t) admits a (proper) sample compression scheme of size O(t), eliminating the logarithmic factors.

Background

This paper constructs proper array sample compression schemes of size O(t log t) for graphs of treewidth t and cliquewidth t, which are tight up to the log factor due to lower bounds of order t. It is unknown whether the logarithmic factor can be removed to achieve optimal linear dependence.