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 ...

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 ...

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 ...

And it’s even harder to tell whether a complicated planar graph stays planar when you start adding edges as you might when planning a new stretch of highway. Computer scientists have been searching ...

The proof is complex and makes use of an excluded minor theorem of Robertson and Seymour, its extension to infinite graphs, Nash-Williams' theory of better-quasi-ordering, especially his infinite tree ...

Let us say that a graph is k- apex if it contains a set of at most k vertices whose removal yields a planar graph. We define the apex number of a graph G as the minimum k for which G is k-apex.