Search results for: Mikhail Lavrov

Items from 1 to 5 out of 5 results

article

Monochromatic connected matchings in 2‐edge‐colored multipartite graphs

József Balogh, Alexandr Kostochka, Mikhail Lavrov, Xujun Liu

Journal of Graph Theory > 100 > 3 > 578 - 607

A matching

M

in a graph

G

is connected if all the edges of

M

are in the same component of

G

. Following Łuczak, there have been many results using the existence of large connected matchings in cluster graphs with respect to regular partitions of large graphs to show the existence of long paths and other structures in these graphs. We prove exact Ramsey‐type bounds on the...

article

Longest cycles in 3‐connected hypergraphs and bipartite graphs

Alexandr Kostochka, Mikhail Lavrov, Ruth Luo, Dara Zirlin

Journal of Graph Theory > 99 > 4 > 758 - 782

In the language of hypergraphs, our main result is a Dirac‐type bound: We prove that every 3‐connected hypergraph

ℋ

with

δ (H) \geq \max {∣ V (H) ∣, \frac{∣ E (H) ∣ + 10}{4}}

has a hamiltonian Berge cycle. This is sharp and refines a conjecture by Jackson from 1981 (in the language of bipartite graphs). Our proofs are in the language of bipartite graphs, since the incidence graph of each hypergraph...

article

Increasing Hamiltonian paths in random edge orderings

Mikhail Lavrov, Po‐Shen Loh

Random Structures & Algorithms > 48 > 3 > 588 - 611

Let f be an edge ordering of K_n: a bijection

E (K_{n}) \to {1, 2, \dots, (\begin{matrix} n \\ 2 \end{matrix})}

. For an edge

e \in E (K_{n})

, we call f(e) the label of e. An increasing path in K_n is a simple path (visiting each vertex at most once) such that the label on each edge is greater than the label on the previous edge. We let S(f) be the number of edges in the longest increasing path. Chvátal and Komlós raised the question of estimating m(n):...

article

Improved upper and lower bounds on a geometric Ramsey problem

Mikhail Lavrov, Mitchell Lee, John Mackey

European Journal of Combinatorics > 2014 > 42 > Complete > 135-144

In Graham and Rothschild (1971), 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}N∗ are 2-colored, there exist 4 coplanar points such that the 6 edges between them are monochromatic. They give an explicit upper bound: N∗≤F(F(F(F(F(F(F(12,3),3),3),3),3),3),3), where F(m,n)=2↑mn, an extremely fast-growing...

article

Person identification from biological motion: Effects of structural and kinematic cues

Nikolaus F. Troje, Cord Westhoff, Mikhail Lavrov

Attention, Perception, & Psychophysics > 2005 > 67 > 4 > 667-675

Human observers are able to identify a person based on his or her gait. However, little is known about the underlying mechanisms and the kind of information used to accomplish such a task. In this study, participants learned to discriminate seven male walkers shown as point-light displays from frontal, half-profile, or profile view. The displays were gradually normalized with respect to size, shape,...

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INFONA - science communication portal

Search results for: Mikhail Lavrov

Monochromatic connected matchings in 2‐edge‐colored multipartite graphs

Longest cycles in 3‐connected hypergraphs and bipartite graphs

Increasing Hamiltonian paths in random edge orderings

Improved upper and lower bounds on a geometric Ramsey problem

Person identification from biological motion: Effects of structural and kinematic cues

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INFONA - science communication portal

Search results for: Mikhail Lavrov

Monochromatic connected matchings in 2‐edge‐colored multipartite graphs

Longest cycles in 3‐connected hypergraphs and bipartite graphs

Increasing Hamiltonian paths in random edge orderings

Improved upper and lower bounds on a geometric Ramsey problem

Person identification from biological motion: Effects of structural and kinematic cues

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