105 citations · 254 across the 20 of their papers we have counts for
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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…
How Ramsey theory can be used to solve Harary's problem for
C. J. Jayawardene, C. C. Rousseau, B. Bollobás
Harary's conjecture for every isolated-free graph G with edges was proved independently by Sidorenko and Goddard and Klietman. In this paper instead of $C_3…
Reconstructing random jigsaws
Paul Balister, Béla Bollobás, Bhargav Narayanan
A colouring of the edges of an grid is said to be \emph{reconstructible} if the colouring is uniquely determined by the multiset of its \emph{tiles}, where the t…
Transference for the Erdős-Ko-Rado theorem
József Balogh, Béla Bollobás, Bhargav Narayanan
For natural numbers with , the Kneser graph is the graph on the family of -element subsets of in which two sets are adjacen…
Limited packings of closed neighbourhoods in graphs
Paul N. Balister, Béla Bollobás, Karen Gunderson
The k-limited packing number, , of a graph , introduced by Gallant, Gunther, Hartnell, and Rall, is the maximum cardinality of a set of vertices of such that eve…
On the stability of the Erdős-Ko-Rado theorem
Béla Bollobás, Bhargav Narayanan, Andrei Raigorodskii
Delete the edges of a Kneser graph independently of each other with some probability: for what probabilities is the independence number of this random graph equal to the independen…
Minimal symmetric differences of lines in projective planes
Paul Balister, Béla Bollobás, Zoltán Füredi +1
Let q be an odd prime power and let f(r) be the minimum size of the symmetric difference of r lines in the Desarguesian projective plane PG(2,q). We prove some results about the fu…
Bootstrap percolation in three dimensions
József Balogh, Béla Bollobás, Robert Morris
By bootstrap percolation we mean the following deterministic process on a graph . Given a set of vertices "infected" at time 0, new vertices are subsequently infected, at ea…
Hereditary properties of ordered graphs
József Balogh, Béla Bollobás, Robert Morris
An ordered graph is a graph together with a linear order on its vertices. A hereditary property of ordered graphs is a collection of ordered graphs closed under taking induced orde…
Hereditary properties of combinatorial structures: posets and oriented graphs
József Balogh, Béla Bollobás, Robert Morris
A hereditary property of combinatorial structures is a collection of structures (e.g. graphs, posets) which is closed under isomorphism, closed under taking induced substructures (…