3 citations · 7 across the 3 of their papers we have counts for
6 papers · 1 filter
Fractional triangle decompositions in almost complete graphs
Vytautas Gruslys, Shoham Letzter
We prove that every -vertex graph with at least edges has a fractional triangle decomposition, for . This is a key ingredient in our proof, giv…
Monochromatic triangle packings in red-blue graphs
Vytautas Gruslys, Shoham Letzter
We prove that in every -edge-colouring of there is a collection of edge-disjoint monochromatic triangles, thus confirming a conjecture of Erdős. We also…
Lagrangians of Hypergraphs II: When colex is best
Vytautas Gruslys, Shoham Letzter, Natasha Morrison
A well-known conjecture of Frankl and Füredi from 1989 states that an initial segment of colex of has the largest Lagrangian of any -uniform hypergraph with hyperedges. We s…
Hypergraph Lagrangians I: the Frankl-Füredi conjecture is false
Vytautas Gruslys, Shoham Letzter, Natasha Morrison
An old and well-known conjecture of Frankl and Füredi states that the Lagrangian of an -uniform hypergraph with edges is maximised by an initial segment of colex. In this pa…
Minimising the number of triangular edges
Vytautas Gruslys, Shoham Letzter
We consider the problem of minimising the number of edges that are contained in triangles, among -vertex graphs with a given number of edges. We prove a conjecture of Füredi and…
Catching a mouse on a tree
Vytautas Gruslys, Arès Méroueh
In this paper we consider a pursuit-evasion game on a graph. A team of cats, which may choose any vertex of the graph at any turn, tries to catch an invisible mouse, which is const…