2 citations · 12 across the 19 of their papers we have counts for
20 papers
The critical activation density in graph bootstrap percolation
Brett Kolesnik, Tamás Makai, Rajko Nenadov +3
In graph bootstrap percolation, edges of an Erdős-Rényi random graph are initially active, and activation spreads to other edges of via the combinatorics…
Canonical labelling of random regular graphs
Mikhail Isaev, Tamás Makai, Brendan McKay +3
We prove that whenever and as , then with high probability for any non-trivial initial colouring, the colour refinement algorithm disti…
Sharp thresholds for higher powers of Hamilton cycles in random graphs
Tamás Makai, Matija Pasch, Kalina Petrova +1
For , we establish that is a sharp threshold for the existence of the -th power of a Hamilton cycle in the binomial random graph model. Our proof…
Enumeration of regular multipartite hypergraphs
Mikhail Isaev, Tamás Makai, Brendan D. McKay
We determine the asymptotic number of regular multipartite hypergraphs, also known as multidimensional binary contingency tables, for all values of the parameters.
Enumeration of dihypergraphs with specified degrees and edge types
Catherine Greenhill, Tamás Makai
A directed hypergraph (dihypergraph) consists of a set of vertices and a set of hyperarcs, where each hyperarc is partitioned into a head and a tail. Directed hypergraphs are usefu…
Limit Laws for Critical Dispersion on Complete Graphs
Umberto De Ambroggio, Tamás Makai, Konstantinos Panagiotou +1
We consider a synchronous process of particles moving on the vertices of a graph , introduced by Cooper, McDowell, Radzik, Rivera and Shiraga (2018). Initially, particles ar…
Bootstrap Percolation on the Binomial Random -uniform Hypergraph
Mihyun Kang, Christoph Koch, Tamás Makai
We investigate the behaviour of -neighbourhood bootstrap percolation on the binomial -uniform random hypergraph for given integers and . In -…
Do random initial degrees suppress concentration in preferential attachment graphs?
T. Makai, F. Polito, L. Sacerdote
We consider the open problem concerning the possible lack of concentration of the degree distribution in preferential attachment graphs with random initial degree, when its distrib…
Dispersion on the Complete Graph
Umberto De Ambroggio, Tamás Makai, Konstantinos Panagiotou
We consider a synchronous process of particles moving on the vertices of a graph , introduced by Cooper, McDowell, Radzik, Rivera and Shiraga (2018). Initially, particles ar…
Degree sequences of sufficiently dense random uniform hypergraphs
Catherine Greenhill, Mikhail Isaev, Tamás Makai +1
We find an asymptotic enumeration formula for the number of simple -uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula…
Resolution of a conjecture on majority dynamics: rapid stabilisation in dense random graphs
Nikolaos Fountoulakis, Mihyun Kang, Tamás Makai
We study majority dynamics on the binomial random graph with and , for some large . In this process, each vertex has a state in a…
The Size of the Giant Joint Component in a Binomial Random Double Graph
Mark Jerrum, Tamás Makai
We study the joint components in a random `double graph' that is obtained by superposing red and blue binomial random graphs on ~vertices. A joint component is a maximal set of…
The sharp threshold for jigsaw percolation in random graphs
Oliver Cooley, Tobias Kapetanopoulos, Tamás Makai
We analyse the jigsaw percolation process, which may be seen as a measure of whether two graphs on the same vertex set are `jointly connected'. Bollobás, Riordan, Slivken and Smith…
Supersaturation Problem for the Bowtie
Mihyun Kang, Tamás Makai, Oleg Pikhurko
The Turán function denotes the maximal number of edges in an -free graph on vertices. We consider the function , the minimal number of copies of in a…
Bootstrap percolation in random -uniform hypergraphs
Mihyun Kang, Christoph Koch, Tamás Makai
We investigate bootstrap percolation with infection threshold on the binomial -uniform random hypergraph in the regime , when…
A phase transition regarding the evolution of bootstrap processes in inhomogeneous random graphs
Nikolaos Fountoulakis, Mihyun Kang, Christoph Koch +1
A bootstrap percolation process on a graph with infection threshold is a dissemination process that evolves in time steps. The process begins with a subset of infected ver…
A simple proof of almost percolation on G(n;p)
Mihyun Kang, Tamás Makai
We consider bootstrap percolation on the binomial random graph with infection threshold , an infection process which starts from a set of initially infect…
Bootstrap percolation on G(n,p) revisited
Mihyun Kang, Tamás Makai
Bootstrap percolation on a graph with infection threshold is an infection process, which starts from a set of initially infected vertices and in each step every v…
Properties of stochastic Kronecker graphs
Mihyun Kang, Michał Karoński, Christoph Koch +1
The stochastic Kronecker graph model introduced by Leskovec et al. is a random graph with vertex set , where two vertices and are connected with probability…
No Dense Subgraphs Appear in the Triangle-free Graph Process
Stefanie Gerke, Tamás Makai
Consider the triangle-free graph process, which starts from the empty graph on vertices and a random ordering of the possible edges; the edges are added in this…