105 citations · 718 across the 103 of their papers we have counts for
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Almost all cancellative triple systems are tripartite
Jozsef Balogh, Dhruv Mubayi
A triple system is cancellative if no three of its distinct edges satisfy . It is tripartite if it has a vertex partition into three parts such that every edge h…
Bootstrap percolation in high dimensions
Jozsef Balogh, Bela Bollobas, Robert Morris
In r-neighbour bootstrap percolation on a graph G, a set of initially infected vertices A \subset V(G) is chosen independently at random, with density p, and new vertices are subse…
Complete Minors, Independent Sets, and Chordal Graphs
Jozsef Balogh, John Lenz, Hehui Wu
The Hadwiger number h(G) of a graph G is the maximum size of a complete minor of G. Hadwiger's Conjecture states that h(G) >= χ(G). Since χ(G) α(G) >= |V(G)|, Hadwiger's Conjecture…
The structure of almost all graphs in a hereditary property
Noga Alon, Jozsef Balogh, Bela Bollobas +1
A hereditary property of graphs is a collection of graphs which is closed under taking induced subgraphs. The speed of ¶is the function n \mapsto |¶_n|, where ¶_n denotes the graph…
Hamilton cycles in random geometric graphs
József Balogh, Béla Bollobás, Michael Krivelevich +2
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penro…