An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph ...
Abstract. The intention of this note is to motivate the researchers to study Hadwiger’s conjecture for circular arc graphs. Let η(G) denote the largest clique minor of a graph G...
N. S. Narayanaswamy, Naveen Belkale, L. Sunil Chan...
For a positive integer k and a graph G, the k-colour graph of G, Ck(G), is the graph that has the proper k-vertex-colourings of G as its vertex set, and two k-colourings are joine...
Luis Cereceda, Jan van den Heuvel, Matthew Johnson
Abstract We study an information-theoretic variant of the graph coloring problem in which the objective function to minimize is the entropy of the coloring. The minimum entropy of ...
We consider two classes of higher order proximity graphs defined on a set of points in the plane, namely, the k-Delaunay graph and the k-Gabriel graph. We give bounds on the follo...