Graph optimisation problems encompass a diverse range of challenges aimed at finding optimal or near‐optimal solutions in networks or graphs. These problems are pivotal in areas such as communication ...

Graph reconfiguration and colouring problems investigate the transition between feasible solutions of a graph colouring instance. The central challenge is to determine a series of elementary vertex ...

A puzzle that has long flummoxed computers and the scientists who program them has suddenly become far more manageable. A new algorithm efficiently solves the graph isomorphism problem, computer ...

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 ...