10 citations · 22 across the 7 of their papers we have counts for
8 papers
Asymptotic normality of the giant component size in a random bipartite graph
Dmitry Shabanov, Pavel Zakharov
This paper studies the giant component of the sparse random bipartite graph , where for a fixed constant . We prove that its size is asymptotically nor…
On the random minimum edge-disjoint spanning trees problem
Dmitry Shabanov, Nikita Zvonkov
It is well known that finding extremal values and structures can be hard in weighted graphs. However, if the weights are random, this problem can become way easier. In this paper,…
Random hypergraphs and property B
Lech Duraj, Jakub Kozik, Dmitry Shabanov
In 1964 Erdős proved that $(1+\oh{1})) \frac{\eul \ln(2)}{4} k^2 2^{k}$ edges are sufficient to build a -graph which is not two colorable. To this day, it is not known whether t…
Number of solutions in abelian groups and application to counting independent sets in hypergraphs
Aliaksei Semchankau, Dmitry Shabanov, Ilya Shkredov
The paper deals with a problem of Additive Combinatorics. Let be a finite abelian group of order . We prove that the number of subset triples $A,B,C\subset {\mathb…
Equitable colorings of hypergraphs with few edges
Margarita Akhmejanova, Dmitry Shabanov
The paper deals with an extremal problem concerning equitable colorings of uniform hyper\-graph. Recall that a vertex coloring of a hypergraph is called proper if there are no…
Coloring hypergraphs with bounded cardinalities of edge intersections
Margarita Akhmejanova, Dmitry Shabanov
The paper deals with an extremal problem concerning colorings of hypergraphs with bounded edge degrees. Consider the family of -simple hypergraphs, in which any two edges do not…
Improved algorithms for colorings of simple hypergraphs and applications
Jakub Kozik, Dmitry Shabanov
The paper deals with extremal problems concerning colorings of hypergraphs. By using a random recoloring algorithm we show that any -uniform simple (i.e. every two distinct edge…
On -colorability of random hypergraphs
Andrei Kupavskii, Dmitry Shabanov
The work deals with the threshold probablity for r-colorability in the binomial model H(n,k,p) of a random k-uniform hypergraph. We prove a lower bound for this threshold which imp…