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 ...

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 ...

Graphs and graph algorithms play a role in modeling them. "You want to get as close to planar as you can in these situations," Yu said. In Graph Theory, wherever K5 or its sprawling relatives TK5s ...

Jacob Holm was flipping through proofs from an October 2019 research paper he and colleague Eva Rotenberg—an associate professor in the department of applied mathematics and computer science at the ...