Extending each of the simply laced Euclidean diagrams A m, m ≥ 1, D m, m ≥ 4, Ẽ 6, Ẽ 7, Ẽ 8 by one vertex, we construct a family of loop-free corank two diagrams à m2, D̃ m2, Ẽ 62, Ẽ 72, Ẽ 82 (called ...

We prove that a properly edge-coloured complete graph Kn has a Hamilton circuit with edges of at least n - √2n distinct colours. This is proved with a method inspired by work on long partial ...

An edge coloring is r-acyclic if it is proper and every cycle C has at least colors. The r-acyclic edge chromatic number of a graph Gis the minimum number of colors needed for any r-acyclic edge ...