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 ...

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 ...

The classical matrix-tree theorem relates the determinant of the combinatorial Laplacian on a graph to the number of spanning trees. We generalize this result to Laplacians on one- and two-dimensional ...