6 citations · 15 across the 10 of their papers we have counts for
8 papers · 1 filter
Flashes and rainbows in tournaments
António Girão, Freddie Illingworth, Lukas Michel +2
Colour the edges of the complete graph with vertex set with an arbitrary number of colours. What is the smallest integer such that if th…
Chromatic number is not tournament-local
António Girão, Kevin Hendrey, Freddie Illingworth +4
Scott and Seymour conjectured the existence of a function such that, for every graph and tournament on the same vertex set, $χ(G) \geqs…
A note on interval colourings of graphs
Maria Axenovich, António Girão, Lawrence Hollom +5
A graph is said to be interval colourable if it admits a proper edge-colouring using palette in which the set of colours incident to each vertex is an interval. The in…
Invertibility of digraphs and tournaments
Noga Alon, Emil Powierski, Michael Savery +2
For an oriented graph and a set , the inversion of in is the digraph obtained by reversing the orientations of the edges of with both endpoints in…
Induced subgraphs of induced subgraphs of large chromatic number
António Girão, Freddie Illingworth, Emil Powierski +4
We prove that, for every graph with at least one edge, there is a constant such that there are graphs of arbitrarily large chromatic number and the same clique number as…
Planar graphs with the maximum number of induced 6-cycles
Michael Savery
For large we determine the maximum number of induced 6-cycles which can be contained in a planar graph on vertices, and we classify the graphs which achieve this maximum. I…
Planar graphs with the maximum number of induced 4-cycles or 5-cycles
Michael Savery
For large we determine exactly the maximum numbers of induced and subgraphs that a planar graph on vertices can contain. We show that uniquely achie…
Chromatic number is Ramsey distinguishing
Michael Savery
A graph is Ramsey for a graph if every colouring of the edges of in two colours contains a monochromatic copy of . Two graphs and are Ramsey equivalent i…