Balogh, BarÃ¡t, Gerbner, GyÃ¡rfÃ¡s, and SÃ¡rkÃ¶zy proposed the following conjecture. Let G be a graph on n vertices with minimum degree at least 3n/4. Then for every 2-edge-colouring of G, the vertex setâ€¦ (More)

Following problems posed by GyÃ¡rfÃ¡s [6], we show that for every r -edge-colouring of Kn there is a monochromatic triple star of order at least n/(r âˆ’ 1), improving RuszinkÃ³â€™s result [10]. An edgeâ€¦ (More)

We prove that the property of containing a k-regular subgraph in the random graph model G(n, p) has a sharp threshold for k â‰¥ 3. We also show how to use similar methods to obtain an easy prove forâ€¦ (More)

In this paper, we study Ramsey-type problems for directed graphs. We first consider the k-colour oriented Ramsey number of H, denoted by âˆ’ â†’r (H, k), which is the least n for which everyâ€¦ (More)

We consider P3-convexity on graphs, where a setU of vertices in a graphG is convex if every vertex not in U has at most one neighbour in U . Tverbergâ€™s theorem states that every set of (k âˆ’ 1)(d + 1)â€¦ (More)