Graph colouring remains a central topic in graph theory, providing the mathematical framework for assigning colours to the elements of a graph under specific constraints. In particular, the colouring ...

This is a preview. Log in through your library . Abstract This paper considers the planar decomposition of a complete bipartite graph, that is, the decomposition of a complete bipartite graph into ...

Two computer scientists found — in the unlikeliest of places — just the idea they needed to make a big leap in graph theory. This past October, as Jacob Holm and Eva Rotenberg were thumbing through a ...

This is a preview. Log in through your library . Abstract Let G be any n-vertex planar graph. We prove that the vertices of G can be partitioned into three sets A, B, C such that no edge joins a ...