We prove that there is an absolute constant C > 0 so that for every natural n there exists a trianglefree regular graph with no independent set of size at least C n log n.
1 The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices2 either G contains G1 or G contains G2, where G denotes the complement of G. In this...
Abstract. In property testing, the goal is to distinguish between objects that satisfy some desirable property and objects that are far from satisfying it, after examining only a s...
In this short note we prove that there is a constant c such that every k-edge-coloring of the complete graph Kn with n 2ck contains a K4 whose edges receive at most two colors. Th...