Geometric intersection graphs form an intriguing class of structures in which vertices represent geometric objects – such as line segments, discs, or curves – and an edge is established between two ...

We derive a formula for the chromatic polynomial of a chordal or a triangulated graph in terms of its maximal cliques. As a corollary we obtain a way to write down an explicit formula for the ...

Properties of the colour-distribution in edge-colourings of graphs are examined. The results are applied in generalizing two theorems of Vizing and in proving the following for m = 5 and 7: If G is ...