Let T be a fixed tournament on k vertices. Let D(n, T) denote the maximum number of orientations of an n-vertex graph that have no copy of T. We prove that D(n, T) = 2tk-1(n) for ...
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...
For two given graphs G1 and G2, the Ramsey number R(G1, G2) is the smallest positive integer n such that for any graph G of order n, either G contains G1 or the complement of G co...
Let X be the random variable that counts the number of triangles in the binomial random graph G(n, p). We show that for some positive constant c, the probability that X deviates f...
: In a previous work, the authors introduced the class of graphs with bounded induced distance of order k, (BID(k) for short) to model non-reliable interconnection networks. A netw...