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 ...

Planar graph algorithms constitute a pivotal area in theoretical computer science, addressing problems where graphs can be drawn on a plane without edge crossings. Among the myriad challenges in this ...

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 study the existence of certain disjoint paths in planar graphs and generalize a theorem of Thomassen on planarizing cycles in surfaces. Results are used to prove that every 5-connected ...

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 ...

For a planar graph, there is always some way to draw it so that the lines from point to point do not cross. In the real world, a microprocessor is sending electrons from point to point down myriad ...