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 ...

A graph is planar if it can be drawn in the plane in such a way that no edges intersect, except of course at a common endvertex. Planar graphs corresponding to the regular polyhedra and other ...

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 ...

The weighted maximal planar graph (WMPG) is practically important in the laying out of facilities in modern manufacturing environments. Given a weighted complete graph, the WMPG seeks to find a ...

We prove that any distributional limit of finite planar graphs in which the degree of the root has an exponential tail is almost surely recurrent. As a corollary, we obtain that the uniform infinite ...

Abstract: In the design of printed circuit boards and integrated circuits, the problem of determining the appropriate wiring direction from pins is addressed by the more complex and difficult problem ...