In this paper, the total chromatic number and fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional ...
We prove that fixed-point logic with counting captures polynomial time on all classes of graphs with excluded minors. That is, for every class C of graphs such that some graph H is...
The f-regressive Ramsey number Rreg f (d, n) is the minimum N such that every colouring of the d-tuples of an N-element set mapping each x1, . . . , xd to a colour ≤ f(x1) contai...
We determine the values of the acyclic chromatic index of a class of graphs referred to as d-dimensional partial tori. These are graphs which can be expressed as the cartesian prod...
Based on an inductive definition of triangulations, a theory of undirected planar graphs is developed in Isabelle/HOL. The proof of the 5 colour theorem is discussed in some detai...