Consider the following question: does every complete geometric graph K2n have a partition of its edge set into n plane spanning trees? We approach this problem from three directio...
An outerplanar (also called circular, convex, one-page) drawing of an n-vertex graph G is a drawing in which the vertices are placed on a circle and each edge is drawn using one s...
Let Kn1,n2,...,nm be a complete m-partite graph with partite sets of sizes n1,n2,...,nm. A complete m-partite graph is balanced if each partite set has n vertices. We denote this c...
In this paper we give a full characterization of the idomatic partitions of the direct product of three complete graphs. We also show how to use such a characterization in order t...
A complete partition of a graph G is a partition of its vertex set in which any two distinct classes are connected by an edge. Let cp(G) denote the maximum number of classes in a ...