António Girão

Generalized Majority Colourings of Digraphs

The purpose of this note is to draw attention to problems related to a concept called majority colouring recently studied by Kreutzer, Oum, Seymour, van der Zypen and Wood. They raised a problem of determining, for a natural number

An improved upper bound on the maximum degree of terminal-pairable complete graphs

k

On a conjecture of Gentner and Rautenbach

, the smallest number

Extension from Precoloured Sets of Edges

m=m(k)

Rainbow saturation of graphs

such that every digraph can be coloured with

Highly linked tournaments with large minimum out-degree

m

Recent Results in Zero-Forcing of Graphs

colours where each vertex has the same colour as at most

A large number of

1/k

m

proportion of its out-neighbours. We show that

-coloured complete infinite subgraphs

m(k)\in\{2k-1,2k\}