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On conjectures concerning the graph grabbing game
Lawrence Hollom
We consider two conjectures made in regard to the graph grabbing game, played on a vertex weighted graph. Seacrest and Seacrest conjectured in 2012 that the first player can win th…
On graphs with maximum difference between game chromatic number and chromatic number
Lawrence Hollom
In the vertex colouring game on a graph , Maker and Breaker alternately colour vertices of from a palette of colours, with no two adjacent vertices allowed the same colo…
A note on monotonicity in Maker-Breaker graph colouring games
Lawrence Hollom
In the Maker-Breaker vertex colouring game, first publicised by Gardner in 1981, Maker and Breaker alternately colour vertices of a graph using a fixed palette, maintaining a prope…
Tight lower bounds for anti-concentration of Rademacher sums and Tomaszewski's counterpart problem
Lawrence Hollom, Julien Portier
In this paper we prove that for every finite Rademacher sum , confirming a conjecture by Hitczenko and Kwapie{ń} from 1994,…
On interval colourings of graphs
Lawrence Hollom, Julien Portier, Leo Versteegen
An interval colouring of a graph is a proper colouring such that the set of colours of edges incident to any given vertex forms an interval of $…
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…
A new proof of the bunkbed conjecture in the limit
Lawrence Hollom
For a finite simple graph , the bunkbed graph is defined to be the product graph . We will label the two copies of a vertex as and .…