Add to ORKGWe 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 hamil-tonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a family of 3-uniform path (cycle) saturated hamiltonian hypergraphs with Ω(n5/2) edges. On the other hand we prove that the number of edges in an r-uniform hamiltonian path (cycle) saturated hypergraph is at least Ω(nr−1)
We show that every $k$-uniform hypergraph on $n$ vertices whose minimum $(k-2)$-degree is at least $...
We say that a k-uniform hypergraph C is a Hamilton cycle of type l, for some 1 ≤ l ≤ k, if there exi...
AbstractUsing a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierst...
AbstractWe say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an op...
AbstractA graph G is said to be hamiltonian path saturated (HPS for short), if G has no hamiltonian ...
AbstractAn r-uniform hypergraph is k-edge-hamiltonian iff it still contains a hamiltonian-chain afte...
We prove for all k\geq 4 and 1\leq \ell <k/2 the sharp minimum (k-2)-degree bound for a k-uniform...
Given $k\ge3$ and $1\leq \ell< k$, an $(\ell,k)$-cycle is one in which consecutive edges, each of si...
AbstractWe prove that any k-uniform hypergraph on n vertices with minimum degree at least n2(k−1)+o(...
Hamiltionian chain is a generalisation of hamiltonian cycles for hypergraphs. Among the several poss...
We define and study a special type of hypergraph. A σ-hypergraph H = H(n, r, q | σ), where σ is a pa...
AbstractWe study sufficient conditions for Hamiltonian cycles in hypergraphs, and obtain both Turán-...
Abstract. We study sufficient conditions for Hamiltonian cycles in hyper-graphs, and obtain both Tur...
Let H be a 3-uniform hypergraph with n vertices. A tight Hamilton cycle C ⊂ H is a collection of n e...
We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-un...
We show that every $k$-uniform hypergraph on $n$ vertices whose minimum $(k-2)$-degree is at least $...
We say that a k-uniform hypergraph C is a Hamilton cycle of type l, for some 1 ≤ l ≤ k, if there exi...
AbstractUsing a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierst...
AbstractWe say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an op...
AbstractA graph G is said to be hamiltonian path saturated (HPS for short), if G has no hamiltonian ...
AbstractAn r-uniform hypergraph is k-edge-hamiltonian iff it still contains a hamiltonian-chain afte...
We prove for all k\geq 4 and 1\leq \ell <k/2 the sharp minimum (k-2)-degree bound for a k-uniform...
Given $k\ge3$ and $1\leq \ell< k$, an $(\ell,k)$-cycle is one in which consecutive edges, each of si...
AbstractWe prove that any k-uniform hypergraph on n vertices with minimum degree at least n2(k−1)+o(...
Hamiltionian chain is a generalisation of hamiltonian cycles for hypergraphs. Among the several poss...
We define and study a special type of hypergraph. A σ-hypergraph H = H(n, r, q | σ), where σ is a pa...
AbstractWe study sufficient conditions for Hamiltonian cycles in hypergraphs, and obtain both Turán-...
Abstract. We study sufficient conditions for Hamiltonian cycles in hyper-graphs, and obtain both Tur...
Let H be a 3-uniform hypergraph with n vertices. A tight Hamilton cycle C ⊂ H is a collection of n e...
We show that, for a natural notion of quasirandomness in k-uniform hypergraphs, any quasirandom k-un...
We show that every $k$-uniform hypergraph on $n$ vertices whose minimum $(k-2)$-degree is at least $...
We say that a k-uniform hypergraph C is a Hamilton cycle of type l, for some 1 ≤ l ≤ k, if there exi...
AbstractUsing a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierst...