10 citations · 19 across the 14 of their papers we have counts for
20 papers
Strong binding numbers and factors
Guantao Chen, Mikhail Lavrov, Yuying Ma +2
Let be a simple graph. The -th neighborhood of a vertex subset , denoted , is the set of vertices that are adjacent to at least vertices in …
Bipartite graphs with the double Hall property
Guantao Chen, Mikhail Lavrov, Yuying Ma +2
The super-neighborhood of a vertex set in a graph , denoted by , is the set of vertices adjacent to at least two vertices in . We say that a bipartite graph $G=(X…
A Hall-type condition for path covers in bipartite graphs
Mikhail Lavrov, Jennifer Vandenbussche
Let be a bipartite graph with bipartition . Inspired by a hypergraph problem, we seek an upper bound on the number of disjoint paths needed to cover all the vertices of…
Online Ramsey numbers of ordered paths and cycles
Felix Christian Clemen, Emily Heath, Mikhail Lavrov
An ordered graph is a graph with a linear ordering on its vertices. The online Ramsey game for ordered graphs and is played on an infinite sequence of vertices; on each tur…
Conditions for a bigraph to be super-cyclic
Alexandr Kostochka, Mikhail Lavrov, Ruth Luo +1
A hypergraph is super-pancyclic if for each with , contains a Berge cycle with base vertex set . We present two…
A Strengthening of the Erdős-Szekeres Theorem
József Balogh, Felix Christian Clemen, Emily Heath +1
The Erdős-Szekeres Theorem stated in terms of graphs says that any red-blue coloring of the edges of the ordered complete graph contains a red copy of the monotone incre…
Longest cycles in 3-connected hypergraphs and bipartite graphs
Alexandr Kostochka, Mikhail Lavrov, Ruth Luo +1
In the language of hypergraphs, our main result is a Dirac-type bound: we prove that every -connected hypergraph with has a h…
Making -Free Graphs -partite
József Balogh, Felix Christian Clemen, Mikhail Lavrov +2
The Erdős-Simonovits stability theorem states that for all ε>0 there exists α>0 such that if G is a K_{r+1}-free graph on n vertices with e(G) > ex(n,K_{r+1}) - αn^2, then one can…
Monochromatic paths and cycles in -edge-colored graphs with large minimum degree
József Balogh, Alexandr Kostochka, Mikhail Lavrov +1
A graph arrows a graph if in every -edge-coloring of there exists a monochromatic copy of . Schelp had the idea that if the complete graph arrows a small gr…
Long monochromatic paths and cycles in 2-edge-colored multipartite graphs
József Balogh, Alexandr Kostochka, Mikhail Lavrov +1
We solve four similar problems: For every fixed and large , we describe all values of such that for every -edge-coloring of the complete -partite grap…
Monochromatic connected matchings in 2-edge-colored multipartite graphs
József Balogh, Alexandr Kostochka, Mikhail Lavrov +1
A matching in a graph is connected if all the edges of are in the same component of . Following Łuczak,there have been many results using the existence of large conn…
Ordered Size Ramsey Number of Paths
József Balogh, Felix Christian Clemen, Emily Heath +1
An ordered graph is a simple graph with an ordering on its vertices. Define the ordered path to be the monotone increasing path with edges. The ordered size Ramsey number…
Monochromatic Hilbert cubes and arithmetic progressions
József Balogh, Mikhail Lavrov, George Shakan +1
The Van der Waerden number denotes the smallest such that whenever is --colored there exists a monochromatic arithmetic progression of length . Similarly,…
Distance-Uniform Graphs with Large Diameter
Mikhail Lavrov, Po-Shen Loh, Arnau Messegué
An -distance-uniform graph is one in which from every vertex, all but an -fraction of the remaining vertices are at some fixed distance , called the critical distance. We…
An upper bound for the Hales-Jewett number HJ(4,2)
Mikhail Lavrov
We show that for at least , any 2-coloring of the -dimensional grid contains a monochromatic combinatorial line. This is a special case of the Hales-Jewett…
Hamiltonian increasing paths in random edge orderings
Mikhail Lavrov, Po-Shen Loh
If the edges of the complete graph are totally ordered, a simple path whose edges are in ascending order is called increasing. The worst-case length of the longest increasing…
Graham's Number is Less Than 2^^^6
Mikhail Lavrov, Mitchell Lee, John Mackey
In [5] Graham and Rothschild consider a geometric Ramsey problem: finding the least n such that if all edges of the complete graph on the points {+1,-1}^n are 2-colored, there exis…
On the S^1 x S^2 HOMFLY-PT invariant and Legendrian links
Mikhail Lavrov, Dan Rutherford
In \cite{GZ}, Gilmer and Zhong established the existence of an invariant for links in which is a rational function in variables and and satisfies the HOMFLY…
On the game chromatic number of sparse random graphs
Alan Frieze, Simi Haber, Mikhail Lavrov
Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wi…
Generalized normal rulings and invariants of Legendrian solid torus links
Mikhail Lavrov, Dan Rutherford
For Legendrian links in the 1-jet space of we show that the 1-graded ruling polynomial may be recovered from the Kauffman skein module. For such links a generalization of the…