منابع مشابه
Hamilton-chain saturated hypergraphs
We say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an open (closed) hamiltonian chain but by adding any new edge we create an open (closed) hamiltonian chain in H. In this paper we ask about the smallest size of an r-uniform hamiltonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a family of 3-uniform path (cycle) saturat...
متن کاملHamilton Saturated Hypergraphs of Essentially Minimum Size
For 1 ≤ ` < k, an `-overlapping cycle is a k-uniform hypergraph in which, for some cyclic vertex ordering, every edge consists of k consecutive vertices and every two consecutive edges share exactly ` vertices. A k-uniform hypergraph H is `-Hamiltonian saturated, 1 ≤ ` ≤ k − 1, if H does not contain an `-overlapping Hamiltonian cycle C (k) n (`) but every hypergraph obtained from H by adding on...
متن کاملUpper Bounds on the Minimum Size of Hamilton Saturated Hypergraphs
For 1 6 ` < k, an `-overlapping k-cycle is a k-uniform hypergraph in which, for some cyclic vertex ordering, every edge consists of k consecutive vertices and every two consecutive edges share exactly ` vertices. A k-uniform hypergraph H is `-Hamiltonian saturated if H does not contain an `-overlapping Hamiltonian k-cycle but every hypergraph obtained from H by adding one edge does contain such...
متن کاملOn hamiltonian chain saturated uniform hypergraphs
We say that a hypergraph H is hamiltonian chain saturated if H does not contain a hamiltonian chain but by adding any new edge we create a hamiltonian chain in H. In this paper we ask about the smallest size of a k-uniform hamiltonian chain saturated hypergraph. We present a construction of a family of k-uniform hamiltonian chain saturated hypergraphs with O(nk−1/2) edges.
متن کاملSaturated and weakly saturated hypergraphs
Lubell proved this by observing that the left-hand side is a probability: it is simply the probability that a maximal chain, chosen uniformly at random, intersects A. The LYM inequality implies that an antichain in P([n]) has size at most ( n bn/2c ) , the size of the ‘middle layer’ in P([n]). (This can also be proved by partitioning P([n]) into ( n bn/2c ) disjoint chains.) Bollobás’ Inequalit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2010
ISSN: 0012-365X
DOI: 10.1016/j.disc.2009.11.014