Supersaturation of even linear cycles in linear hypergraphs
نویسندگان
چکیده
منابع مشابه
Supersaturation of Even Linear Cycles in Linear Hypergraphs
A classic result of Erdős and, independently, of Bondy and Simonovits [3] says that the maximum number of edges in an n-vertex graph not containing C2k, the cycle of length 2k, is O(n1+1/k). Simonovits established a corresponding supersaturation result for C2k’s, showing that there exist positive constants C, c depending only on k such that every n-vertex graph G with e(G) ≥ Cn contains at leas...
متن کاملEven cycles in hypergraphs
A cycle in a hypergraph A is an alternating cyclic sequence A0, v0, A1, v1, . . . , Ak−1, vk−1, A0 of distinct edges Ai and distinct vertices vi of A such that vi ∈ Ai ∩ Ai+1 for all i modulo k. In this paper, we determine the maximum number of edges in hypergraphs on n vertices containing no even cycles.
متن کاملOn Even-Degree Subgraphs of Linear Hypergraphs
A subgraph of a hypergraph H is even if all its degrees are positive even integers, and b-bounded if it has maximum degree at most b. Let fb(n) denote the maximum number of edges in a linear nvertex 3-uniform hypergraph which does not contain a b-bounded even subgraph. In this paper, we show that if b ≥ 12, then n logn 3b log logn ≤ fb(n) ≤ Bn(logn) for some absolute constant B, thus establishi...
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The r-uniform linear k-cycle C k is the r-uniform hypergraph on k(r−1) vertices whose edges are sets of r consecutive vertices in a cyclic ordering of the vertex set chosen in such a way that every pair of consecutive edges share exactly one vertex. Here, we prove a balanced supersaturation result for linear cycles which we then use in conjunction with the method of hypergraph containers to sho...
متن کاملOn 3-uniform hypergraphs without linear cycles∗
We explore properties of 3-uniform hypergraphs H without linear cycles. It is surprising that even the simplest facts about ensuring cycles in graphs can be fairly complicated to prove for hypergraphs. Our main results are that 3-uniform hypergraphs without linear cycles must contain a vertex of strong degree at most two and must have independent sets of size at least 2|V (H)| 5 .
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2020
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548320000206