Henning and Yeo proved a lower bound for the minimum size of a maximum matching in a connected k-regular graphs with n vertices; it is sharp infinitely often. In an earlier paper...
We consider the following question: how large does n have to be to guarantee that in any two-colouring of the edges of the complete graph Kn,n there is a monochromatic Kk,k? In th...
We prove that the total chromatic number of any graph with maximum degree is at most plus an absolute constant. In particular, we show that for su ciently large, the total chromat...
We give the first improvement to the space/approximation trade-off of distance oracles since the seminal result of Thorup and Zwick [STOC'01]. For unweighted graphs, our dista...
Local Search problem, which finds a local minimum of a black-box function on a given graph, is of both practical and theoretical importance to combinatorial optimization, complexi...