Zobrazeno 1 - 10
of 22
pro vyhledávání: '"Joanna Polcyn"'
Autor:
Joanna Polcyn, Andrzej Ruciński
Publikováno v:
Opuscula Mathematica, Vol 37, Iss 4, Pp 597-608 (2017)
We reach beyond the celebrated theorems of Erdȍs-Ko-Rado and Hilton-Milner, and a recent theorem of Han-Kohayakawa, and determine all maximal intersecting triples systems. It turns out that for each \(n\geq 7\) there are exactly 15 pairwise non-isom
Externí odkaz:
https://doaj.org/article/9975612cc1674cc18e419cbe6a5651d6
Publikováno v:
Combinatorica. 42:115-136
One of the oldest results in modern graph theory, due to Mantel, asserts that every triangle-free graphs on $n$ vertices has at most $\lfloor n^2/4\rfloor$ edges. About half a century later Andr\'asfai studied dense triangle-free graphs and proved th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7b143a8c657fa2b8d99957549bf9d21a
https://doi.org/10.1007/s00493-021-4340-0
https://doi.org/10.1007/s00493-021-4340-0
Publikováno v:
Journal of Graph Theory. 98:460-498
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f1a3784caca3af83a4fa79f305b6e417
https://doi.org/10.1002/jgt.22709
https://doi.org/10.1002/jgt.22709
Publikováno v:
Journal of Graph Theory. 98:57-80
Given positive integers $n\ge s$, we let ${\mathrm{ex}}(n,s)$ denote the maximum number of edges in a triangle-free graph $G$ on $n$ vertices with $\alpha(G)\le s$. In the early sixties Andr\'{a}sfai conjectured that for $n/3
Comment: Revised ac
Comment: Revised ac
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::28b3994766ccb1b10790f005c79caaf5
https://doi.org/10.1002/jgt.22682
https://doi.org/10.1002/jgt.22682
Autor:
Joanna Polcyn, Bjarne Schülke, Vojtěch Rödl, Andrzej Ruciński, Mathias Schacht, Christian Reiher
Publikováno v:
Acta Mathematica Hungarica
We show that every 4-uniform hypergraph with $n$ vertices and minimum pair degree at least $(5/9+o(1))n^2/2$ contains a tight Hamiltonian cycle. This degree condition is asymptotically optimal.
Dedicated to Endre Szemer\'edi on the occasion of h
Dedicated to Endre Szemer\'edi on the occasion of h
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0e8ef88951c461b87cc435123360a535
https://doi.org/10.1007/s10474-020-01078-7
https://doi.org/10.1007/s10474-020-01078-7
Bermond and Thomassen conjectured that every digraph with minimum outdegree at least $2k-1$ contains $k$ vertex disjoint cycles. So far the conjecture was verified for $k\le 3$. Here we generalise the question asking for all outdegree sequences which
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8e9d97fb6ac190d9d1364ab2ac7c27cf
We find the exact value of the Ramsey number $R(C_{2\ell},K_{1,n})$, when $\ell$ and $n=O(\ell^{10/9})$ are large. Our result is closely related to the behaviour of Tur\'an number $ex(N, C_{2\ell})$ for an even cycle whose length grows quickly with $
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7b7812d4f0af428f722b40506e734939
We show that every $k$-uniform hypergraph on $n$ vertices whose minimum $(k-2)$-degree is at least $(5/9+o(1))n^2/2$ contains a Hamiltonian cycle. A construction due to Han and Zhao shows that this minimum degree condition is optimal. The same result
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2d4f0fbe95a8b11d327a2a7eb7d23850
Publikováno v:
European Journal of Combinatorics. 71:43-50
We show that there exists an absolute constant A such that for each k ≥ 2 and every coloring of the edges of the complete k -uniform hypergraph on A r vertices with r colors, r ≥ r k , one of the color classes contains a loose path of length thre
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f15d4293eff58a93dac2d13094785497
https://doi.org/10.1016/j.ejc.2018.02.033
https://doi.org/10.1016/j.ejc.2018.02.033
Autor:
Joanna Polcyn, Tomasz Łuczak
Publikováno v:
Discrete Mathematics. 341:1270-1274
We study the Ramsey number for the 3-uniform loose path of length three, P 3 3 , and n colors. We show that R ( P 3 3 ; n ) ≤ λ 0 n + 7 n , for some explicit constant λ 0 = 1 . 97466 … .
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::40f1e6d1a50162872e16338bdf2e7c05
https://doi.org/10.1016/j.disc.2018.01.015
https://doi.org/10.1016/j.disc.2018.01.015