An acyclic edge colouring of a graph is a proper edge colouring having no 2-coloured cycle, that is, a colouring in which the union of any two colour classes forms a linear forest...
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 ...
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...
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph...
An edge-operation on a graph G is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs G, the editing distance fro...