5 citations · 5 across the 2 of their papers we have counts for
5 papers
Upper density of monochromatic paths in edge-coloured infinite complete graphs and bipartite graphs
A. Nicholas Day, Allan Lo
The upper density of an infinite graph with is defined as . Let $K…
Extremal problems for multigraphs
A. Nicholas Day, Victor Falgas-Ravry, Andrew Treglown
An -graph is an -vertex multigraph in which every -set of vertices spans at most edges. Turán-type questions on the maximum of the sum of the edge multiplicities…
On a Conjecture of Nagy on Extremal Densities
A. Nicholas Day, Amites Sarkar
We disprove a conjecture of Nagy on the maximum number of copies N(G,H) of a fixed graph G in a large graph H with prescribed edge density. Nagy conjectured that for all G, the qua…
Maker-Breaker Percolation Games II: Escaping to Infinity
A. Nicholas Day, Victor Falgas-Ravry
Let be an infinite connected graph, and let be a vertex of . We consider the following positional game. Two players, Maker and Breaker, play in alternating turns. Init…
Saturated Graphs of Prescribed Minimum Degree
A. Nicholas Day
A graph is -saturated if it contains no copy of as a subgraph but the addition of any new edge to creates a copy of . In this paper we are interested in the funct…