Andrzej Zak

Learn More
A graph G is called (H; k)-vertex stable if G contains a subgraph isomorphic to H ever after removing any of its k vertices. Q(H; k) denotes the minimum size among the sizes of all (H; k)-vertex stable graphs. In this paper we complete the characterization of (Km,n; 1)-vertex stable graphs with minimum size. Namely, we prove that for m ≥ 2 and n ≥ m + 2,(More)
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 hamil-tonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a(More)
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(More)