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...

A graph G is H-saturated if G does not contain H as a subgraph but for any nonadjacent vertices u and v, G+uv containsH as a subgraph. The parameter sat(H, n) is theminimum number of edges in an H-saturated graph of order n. In this paper, we determine sat(H, n) for sufficiently large nwhen H is a union of cliques of the same order, an arbitrary union of two cliques and a generalized friendship...

In this paper we give tight lower bounds on the size of the visibility graph, the contracted visibility graph, and the bar-visibility graph of n disjoint line segments in the plane, according to their vertex-connectivity.

In traditional multihop network broadcast problems, in which a message beginning at one node is efficiently relayed to all others, cost models typically used involve a charge for each unicast or each broadcast. These settings lead to a minimum spanning tree (MST) problem or the Connected Dominating Set (CDS) problem, respectively. Neglected, however, is the study of intermediate models in which...

This paper shows that the Discrete Logarithm Problem is in ZPP (where MCSP is the Minimum Circuit Size Problem). This result improves the previous bound that the Discrete Logarithm Problem is in BPP Allender et al. (2006). In doing so, this paper helps classify the relative difficulty of the Minimum Circuit Size Problem.

The main part of gossip schemes are the kernels of their minimal orders. We give a complete characterization of all kernels that may appear in gossip schemes on simple graphs with a minimum number of calls. As consequences we prove several results on gossip schemes, e.g. the minimum number of rounds of a gossip scheme with a minimum number of calls is computed. Moreover, in the new context we g...

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We focus on confidence-bounded association rules; we model a rather practical situation in which the confidence threshold is fixed by the user, as usually happens in applications. Within this model, we study notions of redundancy among association rules from a fundamental perspective: we discuss several existing alternative definitions and provide new characterizations and relationships between...

In this paper we describe a new model and algorithm for computing minimum-size prime implicants of Boolean functions. The computation of minimum-size prime implicants has several applications in different areas, including Electronic Design Automation (EDA), Non-Monotonic Reasoning, Logical Inference, among others. For EDA, one significant and immediate application is the computation of minimum-...