Zobrazeno 1 - 10
of 113
pro vyhledávání: '"Tyomkyn, Mykhaylo"'
Autor:
Skokan, Jozef, Tyomkyn, Mykhaylo
In new progress on conjectures of Stein, and Addario-Berry, Havet, Linhares Sales, Reed and Thomass\'e, we prove that every oriented graph with all in- and out-degrees greater than 5k/8 contains an alternating path of length k. This improves on previ
Externí odkaz:
http://arxiv.org/abs/2406.03166
An independent vertex subset $S$ of the directed graph $G$ is a kernel if the set of out-neighbors of $S$ is $V(G)\setminus S$. An independent vertex subset $Q$ of $G$ is a quasi-kernel if the union of the first and second out-neighbors contains $V(G
Externí odkaz:
http://arxiv.org/abs/2307.04112
Autor:
Shapira, Asaf, Tyomkyn, Mykhaylo
The celebrated Brown-Erd\H{o}s-S\'os conjecture states that for every fixed $e$, every $3$-uniform hypergraph with $\Omega(n^2)$ edges contains $e$ edges spanned by $e+3$ vertices. Up to this date all the approaches towards resolving this problem rel
Externí odkaz:
http://arxiv.org/abs/2301.07758
Given an $r$-edge-coloring of the complete graph $K_n$, what is the largest number of edges in a monochromatic connected component? This natural question has only recently received the attention it deserves, with work by two disjoint subsets of the a
Externí odkaz:
http://arxiv.org/abs/2204.11360
Autor:
Shapira, Asaf, Tyomkyn, Mykhaylo
Given a fixed hypergraph $H$, let $\mbox{wsat}(n,H)$ denote the smallest number of edges in an $n$-vertex hypergraph $G$, with the property that one can sequentially add the edges missing from $G$, so that whenever an edge is added, a new copy of $H$
Externí odkaz:
http://arxiv.org/abs/2111.02373
Given $q$-uniform hypergraphs ($q$-graphs) $F,G$ and $H$, where $G$ is a spanning subgraph of $F$, $G$ is called weakly $H$-saturated in $F$ if the edges in $E(F)\setminus E(G)$ admit an ordering $e_1,\dots, e_k$ so that for all $i\in [k]$ the hyperg
Externí odkaz:
http://arxiv.org/abs/2109.03703
Autor:
Conlon, David, Tyomkyn, Mykhaylo
We show that every two-colouring of the edges of the complete graph $K_n$ contains a monochromatic trail or circuit of length at least $2n^2/9 +o(n^2)$, which is asymptotically best possible.
Comment: 3 pages
Comment: 3 pages
Externí odkaz:
http://arxiv.org/abs/2109.02633
Autor:
Shapira, Asaf, Tyomkyn, Mykhaylo
The pantograph differential equation and its solution, the deformed exponential function, are remarkable objects that appear in areas as diverse as combinatorics, number theory, statistical mechanics, and electrical engineering. In this article we de
Externí odkaz:
http://arxiv.org/abs/2101.08173
Autor:
Conlon, David, Tyomkyn, Mykhaylo
For a fixed graph $H$, what is the smallest number of colours $C$ such that there is a proper edge-colouring of the complete graph $K_n$ with $C$ colours containing no two vertex-disjoint colour-isomorphic copies, or repeats, of $H$? We study this fu
Externí odkaz:
http://arxiv.org/abs/2002.00921
Autor:
Tyomkyn, Mykhaylo
Publikováno v:
Combinator. Probab. Comp. 30 (2021) 153-162
We prove that any $n$-vertex graph whose complement is triangle-free contains $n^2/12-o(n^2)$ edge-disjoint triangles. This is tight for the disjoint union of two cliques of order $n/2$. We also prove a corresponding stability theorem, that all large
Externí odkaz:
http://arxiv.org/abs/2001.00763