4 citations · 14 across the 23 of their papers we have counts for
17 papers · 1 filter
Upper bounds for multicolour Ramsey numbers
Paul Balister, Béla Bollobás, Marcelo Campos +5
The -colour Ramsey number is the minimum such that every -colouring of the edges of the complete graph on vertices contains a monochroma…
Intersections of iterated shadows
Hou Tin Chau, David Ellis, Marius Tiba
We show that if with measure bounded away from zero and from one, then the -iterated upper shadows of and $\mathc…
On Ruzsa's discrete Brunn-Minkowski conjecture
Peter van Hintum, Peter Keevash, Marius Tiba
We prove a conjecture by Ruzsa from 2006 on a discrete version of the Brunn-Minkowski inequality, stating that for any and with not contained in…
Erdős covering systems
Paul Balister, Béla Bollobás, Robert Morris +2
A covering system is a finite collection of arithmetic progressions whose union is the set of integers. The study of these objects was initiated by Erdős in 1950, and over the foll…
Large sumsets from medium-sized subsets
Bela Bollobas, Imre Leader, Marius Tiba
The classical Cauchy--Davenport inequality gives a lower bound for the size of the sum of two subsets of , where is a prime. Our main aim in this paper is to pro…
Large sumsets from small subsets
Bela Bollobas, Imre Leader, Marius Tiba
In this paper we start to investigate a new body of questions in additive combinatorics. The fundamental Cauchy--Davenport theorem gives a lower bound on the size of a sumset A+B f…
A strengthening of Freiman's 3k-4 theorem
Bela Bollobas, Imre Leader, Marius Tiba
In its usual form, Freiman's 3k-4 theorem states that if A and B are subsets of the integers of size k with small sumset (of size close to 2k) then they are very close to arithmeti…
Radius, Girth and Minimum Degree
Vojtěch Dvořák, Peter van Hintum, Amy Shaw +1
Given a connected graph on vertices, with minimum degree and girth at least , what is the maximum radius this graph can have? Erdős, Pach, Pollack a…
Improved Bound for Tomaszewski's Problem
Vojtěch Dvořák, Peter van Hintum, Marius Tiba
In 1986, Tomaszewski made the following conjecture. Given real numbers with , then of the signed sums $\pm a_{1} \pm ... \p…
Multicolour chain avoidance in the boolean lattice
Hunter Spink, Marius Tiba
Given a collection of colored chain posets, we estimate the number of colored subsets of the boolean lattice which avoid all chains in the collection.
The structure and number of Erdős covering systems
Paul Balister, Béla Bollobás, Robert Morris +2
Introduced by Erdős in 1950, a covering system of the integers is a finite collection of arithmetic progressions whose union is the set . Many beautiful questions and c…
Judiciously 3-partitioning 3-uniform hypergraphs
Hunter Spink, Marius Tiba
Bollobás, Reed and Thomason proved every -uniform hypergraph with edges has a vertex-partition such that each part m…
Solvability of Mazes by Blind Robots
Stefan David, Marius Tiba
In this paper we introduce and investigate a new type of automata which turns out to be rich in deep and complex phenomena. For our model, a maze is a countable strongly connected…
Strong Ramsey Games in Unbounded Time
Stefan David, Ivailo Hartarsky, Marius Tiba
For two graphs and the strong Ramsey game on the board and with target is played as follows. Two players alternately claim edges of . The firs…
Symmetric Chain Decompositions of Products of Posets with Long Chains
Stefan David, Hunter Spink, Marius Tiba
We ask if there exists a symmetric chain decomposition of the cuboid such that no chain is "taut", i.e. no chain has a subchain of the form $(a_1,\ldots, a_k,0)\prec…
Geometric Symmetric Chain Decompositions
Stefan David, Hunter Spink, Marius Tiba
We create a framework for studying symmetric chain decompositions of families of finite posets based on the geometry of polytopes. Our framework unifies almost all known results re…
An algorithm to prescribe the configuration of a finite graph
Paul Baird, Marius Tiba
We provide algorithms involving edge slides, for a connected simple graph to evolve in a finite number of steps to another connected simple graph in a prescribed configuration, and…