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-...
We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For kdegenerate graphs with...