7 citations · 18 across the 18 of their papers we have counts for
18 papers
The sandglass conjecture beyond cancellative pairs
Adva Mond, Victor Souza, Leo Versteegen
The sandglass conjecture, posed by Simonyi, states that if a pair of families of subsets of is recovering then . We improve the best known upper bo…
On norming systems of linear equations
Seokjoon Cho, David Conlon, Joonkyung Lee +2
A system of linear equations is said to be norming if a natural functional giving a weighted count for the set of solutions to the system can be used to define a n…
Packing and finding paths in sparse random graphs
Vesna Iršič, Julien Portier, Leo Versteegen
Let be a (hidden) Erdős-Rényi random graph with for some fixed constant . Ferber, Krivelevich, Sudakov, and Vieira showed tha…
A proof of a conjecture of Erdős and Gyárfás on monochromatic path covers
Alexey Pokrovskiy, Leo Versteegen, Ella Williams
In 1995, Erdős and Gyárfás proved that in every -edge-coloured complete graph on vertices, there exists a collection of monochromatic paths, all of the same colo…
Around the positive graph conjecture
David Conlon, Joonkyung Lee, Leo Versteegen
A graph is said to be positive if the homomorphism density is non-negative for all weighted graphs . The positive graph conjecture proposes a characterisation of su…
Upper bounds for linear graph codes
Leo Versteegen
A linear graph code is a family of graphs on vertices with the property that the symmetric difference of the edge sets of any two graphs in is also…
Strongly common graphs with odd girth are cycles
Leo Versteegen
A graph is called strongly common if for every coloring of with two colors, the number of monochromatic copies of is at least the number of monochromatic copies o…
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…
The structure of large sum-free sets in
Leo Versteegen
A set is sum-free if does not intersect . If , the maximal size of a sum-free in is known to be $(p^n+p^{n-1})…
Progress towards the 1/2-Conjecture for the domination game
Julien Portier, Leo Versteegen
The domination game is played on a graph by two players, Dominator and Staller, who alternate in selecting vertices until each vertex in the graph is contained in the close…
A proof of the 3/4 conjecture for the total domination game
Julien Portier, Leo Versteegen
In this paper we describe a strategy for Dominator that finishes the total domination game in at most moves for every graph on vertices without any isolated vertices…
A proof of the 3/5-conjecture in the domination game
Leo Versteegen
The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph . A vertex is said to be dominated if it has…
On the number of minimum dominating sets and total dominating sets in forests
Jan Petr, Julien Portier, Leo Versteegen
We show that the maximum number of minimum dominating sets of a forest with domination number is at most and construct for each a tree with domination number $…
A note on Cops and Robbers, independence number, domination number and diameter
Jan Petr, Julien Portier, Leo Versteegen
We study relations between diameter , domination number , independence number and cop number of a connected graph , showing (i.) $c(G) \leq α(G)-\lfloo…
Improved bounds for the dimension of divisibility
Victor Souza, Leo Versteegen
The dimension of a partially-ordered set is the smallest integer such that one can embed into a product of linear orders. We prove that the dimension of the divisib…
A faster algorithm for Cops and Robbers
Jan Petr, Julien Portier, Leo Versteegen
We present an algorithm of time complexity deciding whether a graph on vertices is -copwin. The fastest algorithm thus far had time complexity $O(n^{2k+2})…
Common and Sidorenko equations in Abelian groups
Leo Versteegen
A linear configuration is said to be common in a finite Abelian group if for every 2-coloring of the number of monochromatic instances of the configuration is at least as l…