Zobrazeno 1 - 10
of 19
pro vyhledávání: '"Mykhaylo Tyomkyn"'
Autor:
David Conlon, Mykhaylo Tyomkyn
For a fixed graph H, what is the smallest number of colors C such that there is a proper edge-coloring of the complete graph K_n with C colors containing no two vertex-disjoint color-isomorphic copies, or repeats, of H? We study this function and its
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::29a67a0cb6c34a98c62797b6124edf6b
https://resolver.caltech.edu/CaltechAUTHORS:20200914-134941914
https://resolver.caltech.edu/CaltechAUTHORS:20200914-134941914
Publikováno v:
Mathematical Proceedings of the Cambridge Philosophical Society. 169:323-333
The conjecture of Brown, Erdős and Sós from 1973 states that, for any k ≥ 3, if a 3-uniform hypergraph H with n vertices does not contain a set of k +3 vertices spanning at least k edges then it has o(n2) edges. The case k = 3 of this conjecture
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b32ffd5b88229db874f0ffd7b9fc7382
https://doi.org/10.1017/s0305004119000203
https://doi.org/10.1017/s0305004119000203
Autor:
Mykhaylo Tyomkyn, Asaf Shapira
Publikováno v:
The American Mathematical Monthly
article-version (VoR) Version of Record
article-version (VoR) Version of Record
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:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9c6e6bb84ae32ec4c63276a4d39324fd
http://arxiv.org/abs/2101.08173
http://arxiv.org/abs/2101.08173
Publikováno v:
Journal of Combinatorial Theory, Series B
The Erdős–Hajnal Theorem asserts that non-universal graphs, that is, graphs that do not contain an induced copy of some fixed graph H, have homogeneous sets of size significantly larger than one can generally expect to find in a graph. We obtain t
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::ba3807bc0e2495499f82eb6ddcb21f0f
Autor:
Mykhaylo Tyomkyn
We prove that any n-vertex graph whose complement is triangle-free contains n2/12 – o(n2) 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 gra
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5ce69474c44124f879a4c150d6e1e52c
http://arxiv.org/abs/2001.00763
http://arxiv.org/abs/2001.00763
Publikováno v:
Transactions of the American Mathematical Society. 371:4655-4742
We develop a new method for constructing approximate decompositions of dense graphs into sparse graphs and apply it to long-standing decomposition problems. For instance, our results imply the following. Let G G be a quasi-random n n -vertex graph an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b4b847f8fb6a6fa808c7531c1de5d4ec
https://doi.org/10.1090/tran/7411
https://doi.org/10.1090/tran/7411
Autor:
Mykhaylo Tyomkyn
Publikováno v:
Journal of the London Mathematical Society. 96:584-600
Frankl and Furedi conjectured in 1989 that the maximum Lagrangian of all $r$-uniform hypergraphs of fixed size $m$ is realised by the initial segment of the colexicographic order. In particular, in the principal case $m=\binom{t}{r}$ their conjecture
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::93055c18b96ee04aa08bcb7a62d05aeb
https://doi.org/10.1112/jlms.12082
https://doi.org/10.1112/jlms.12082
Autor:
Dan Hefetz, Mykhaylo Tyomkyn
Publikováno v:
Electronic Notes in Discrete Mathematics
In 1975 Pippenger and Golumbic proved that any graph on n vertices admits at most 2 e ( n / k ) k induced k-cycles. This bound is larger by a multiplicative factor of 2e than the simple lower bound obtained by a blow-up construction. Pippenger and Go
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https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e29dda9aad29c0e27111b93eb86b7508
https://doi.org/10.1016/j.jctb.2018.04.008
https://doi.org/10.1016/j.jctb.2018.04.008
Publikováno v:
Combinatorics, Probability and Computing
The inducibility of a graph $H$ measures the maximum number of induced copies of $H$ a large graph $G$ can have. Generalizing this notion, we study how many induced subgraphs of fixed order $k$ and size $\ell$ a large graph $G$ on $n$ vertices can ha
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b860e8ab9e3aac17b3f954624664c405
http://arxiv.org/abs/1805.06848
http://arxiv.org/abs/1805.06848
Autor:
Andrew J. Uzzell, Mykhaylo Tyomkyn
Publikováno v:
Electronic Notes in Discrete Mathematics. 49:433-440
We study maximal $K_{r+1}$-free graphs $G$ of almost extremal size—typically, $e(G)=\operatorname{ex}(n,K_{r+1})-O(n)$. We show that any such graph $G$ must have a large amount of `symmetry': in particular, all but very few vertices of $G$ must hav
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6ad7b55ade70be736d25cbf78c075c00
https://doi.org/10.1016/j.endm.2015.06.061
https://doi.org/10.1016/j.endm.2015.06.061