منابع مشابه
On 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 .
متن کاملThe Number of Hypergraphs without Linear Cycles
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 tight cycles in hypergraphs
A tight k-uniform `-cycle, denoted by TC ` , is a k-uniform hypergraph whose vertex set is v0, · · · , v`−1, and the edges are all the k-tuples {vi, vi+1, · · · , vi+k−1}, with subscripts modulo k. Motivated by a classic result in graph theory that every n-vertex cycle-free graph has at most n− 1 edges, Sós and, independently, Verstraëte asked whether for every integer k, a k-uniform n-vertex h...
متن کاملThe maximum size of hypergraphs without generalized 4-cycles
Let fr(n) be the maximum number of edges in an r-uniform hypergraph on n vertices that does not contain four edges A,B,C, D with A ∪ B = C ∪D and A ∩ B = C ∩D = ∅. This problem was stated by Erdős [Congres. Numer., 19 (1977) 3–12]. It can be viewed as a generalization of the Turán problem for the 4-cycle to hypergraphs. Let φr = lim supn→∞ fr(n)/ ( n r−1 ) . Füredi [Combinatorica, 4 (1984) 161–...
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.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1976
ISSN: 0095-8956
DOI: 10.1016/0095-8956(76)90070-8