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 ...

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 ...

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 ...