Edge colouring is a fundamental concept in graph theory whereby colours are assigned to the edges of a graph such that no two adjacent edges share the same colour. This process is central to numerous ...

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 ...

If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...

Let G = (V(G), E(G)) be a graph. A set S ⊆ E(G) is an edge k-cut in G if the graph G − S = (V(G), E(G) \ S) has at least k connected components. The generalized k-edge connectivity of a graph G, ...

It is known that there exist many pairs of nonisomorphic graphs which have the same set of eigenvalues, even when counting multiplicities. Such graphs have identical characteristic polynomials (of ...

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 Game of Cycles, introduced by Su in 2020, is played on a simple connected planar graph together with its bounded cells, and players take turns marking edges with arrows according to a sink-source ...

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. It started with a bet. In the late 1980s, at a ...