A geometric graph is a graph G = (V, E) drawn in the plane, such that V is a point set in general position and E is a set of straight-line segments whose endpoints belong to V . W...
In this paper, we study the Minimum Sum Set Coloring (MSSC) problem which consists in assigning a set of x(v) positive integers to each vertex v of a graph so that the intersectio...
Abstract. We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph G and its directed line graph LG. The sandpile group is an abelian group associa...
Given a Morse function over a 2-manifold with or without boundary, the Reeb graph is obtained by contracting the connected components of the level sets to points. We prove tight u...
Kree Cole-McLaughlin, Herbert Edelsbrunner, John H...
We study vertex colorings of the square G2 of an outerplanar graph G. We find the optimal bound of the inductiveness, chromatic number and the clique number of G2 as a function of...