Let K− r denote the graph obtained from Kr by deleting one edge. We show that for every integer r ≥ 4 there exists an integer n0 = n0(r) such that every graph G whose order n â...
We introduce a new graph parameter, called the Grothendieck constant of a graph G = (V, E), which is defined as the least constant K such that for every A : E R, sup f:V S|V |-1 ...
Noga Alon, Konstantin Makarychev, Yury Makarychev,...
Given a simple graph G, a harmonious coloring of G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number i...
We show that if a graph G has the property that all subsets of vertices of size n/4 contain the "correct" number of triangles one would expect to find in a random graph ...
We study a random graph Gn that combines certain aspects of geometric random graphs and preferential attachment graphs. The vertices of Gn are n sequentially generated points x1, ...