We introduce an algorithm that embeds a given 3-connected planar graph as a convex 3-polytope with integer coordinates. The size of the coordinates is bounded by O(27.55n ) = O(18...
A proper vertex coloring of a graph is equitable if the sizes of its color classes differ by at most one. In this note, we prove that if G is a graph such that for each edge xy E...
Abstract. A one-player, finite, probabilistic game with perfect information can be presented as a bipartite graph. For one-player Can't Stop, the graph is cyclic and the chall...
Given a graph G = (V, E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2, . . . ,...
For a simple path Pr on r vertices, the square of Pr is the graph P2 r on the same set of vertices of Pr , and where every pair of vertices of distance two or less in Pr is connec...