The Ramsey Number of Fano Plane Versus Tight Path
نویسندگان
چکیده
منابع مشابه
Stability of the path-path Ramsey number
Here we prove a stability version of a Ramsey-type Theorem for paths. Thus in any 2-coloring of the edges of the complete graph Kn we can either find a monochromatic path substantially longer than 2n/3, or the coloring is close to the extremal coloring.
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Moreover, the only extremal configuration can be obtained by partitioning an n-element set into two almost equal parts, and taking all the triples that intersect both of them. This extends an earlier result of de Caen and Füredi, and proves an old conjecture of V. Sós. In addition, we also prove a stability result for the Fano plane, which says that a 3-uniform hypergraph with density close to ...
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For s ≥ 4, the 3-uniform tight cycle C s has vertex set corresponding to s distinct points on a circle and edge set given by the s cyclic intervals of three consecutive points. For fixed s ≥ 4 and s 6≡ 0 (mod 3) we prove that there are positive constants a and b with 2 < r(C s ,K 3 t ) < 2 bt log . The lower bound is obtained via a probabilistic construction. The upper bound for s > 5 is proved...
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The 3-uniform tight cycle C s has vertex set Zs and edge set {{i, i+ 1, i+ 2} : i ∈ Zs}. We prove that for every s 6≡ 0 (mod 3) and s ≥ 16 or s ∈ {8, 11, 14} there is a cs > 0 such that the 3-uniform hypergraph Ramsey number r(C s ,K n ) satisfies r(C s ,K n ) < 2cn . This answers in strong form a question of the author and Rödl who asked for an upper bound of the form 2n 1+ǫs for each fixed s ...
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Let C (3) n denote the 3-uniform tight cycle, that is the hypergraph with vertices v1, . . . , vn and edges v1v2v3, v2v3v4, . . . , vn−1vnv1, vnv1v2. We prove that the smallest integer N = N(n) for which every red-blue coloring of the edges of the complete 3-uniform hypergraph with N vertices contains a monochromatic copy of C (3) n is asymptotically equal to 4n/3 if n is divisible by 3, and 2n...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/8374