# Search results for: Mikhail Lavrov

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

*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...

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

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

*f*be an edge ordering of

*K*

_{n}: a bijection $E\left({K}_{n}\right)\to \{1,2,\dots ,\left(\begin{array}{c}n\\ 2\end{array}\right)\}$. For an edge $e\in E\left({K}_{n}\right)$, 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*):...

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

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