For a given connected graph G on n vertices and m edges, we prove that its independence number α(G) is at least ((2m+n+2) -((2m+n+2)2 -16n2 )½ )/8. Keywords : independence numbe...
Let G be a simple graph with n vertices and m edges. Let ω(G) and α(G) be the numbers of vertices of the largest clique and the largest independent set in G, respectively. In th...
Abstract. A solid object in 3-dimensional space may be described by a collection of all its topologically distinct 2-dimensional appearances, its aspect graph. In this paper, we st...
A topological graph is called k-quasi-planar, if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a kquasi-...
The Zarankiewicz number z(s, m) is the maximum number of edges in a subgraph of K(s, s) that does not contain K(m, m) as a subgraph. The bipartite Ramsey number b(m, n) is the lea...
Wayne Goddard, Michael A. Henning, Ortrud R. Oelle...