The smallest n such that every colouring of the edges of Kn must contain a monochromatic star K1,s+1 or a properly edge-coloured Kt is denoted by f(s, t). Its existence is guarant...
For a simple path Pr on r vertices, the square of Pr is the graph P2 r on the same set of vertices of Pr , and where every pair of vertices of distance two or less in Pr is connec...
Let G = (V, E) be any d-regular graph with girth g on n vertices, for d ≥ 3. This note shows that G has a maximum matching which includes all but an exponentially small fraction...