On a problem of K. Zarankiewicz

TL;DR: It is shown that the difference between the smallest cancellation-free circuit and the smallest linear circuit can be a factor Ω(n/log2n) and this result improves on a recent result by Sergeev and Gashkov who have studied a similar problem.

TL;DR: This work considers reconfiguration variants of three fundamental underlying graph vertex-subset problems, namely Independent Set, Dominating Set, and Connected Dominating set, and surveys both older and more recent work on the parameterized complexity of all three problems when parameterized by the number of tokens k.

TL;DR: The size Ramsey number of graphs with bounded treewidth and bounded degree was shown to be linear in this paper for any positive integer k and positive integer s, where k is the number of vertices in a tree.

TL;DR: The sum of the bandwidths of a graph and its complement is almost always at least ; it is always at most 2n−4 log 2n+o(log n) and the proofs involve improving the bounds on the Ramsey and Turán numbers of the “halfgraph”.