A conjecture of Berge about linear hypergraphs and Steiner systems S(2,4,v)

AbstractA famous conjecture of Berge about linear hypergraphs is studied. It is proved that all nearly resolvable Steiner systems S(2,4,v) and all almost nearly resolvable S(2,4,v) verify this conjecture

The Spectrum of Balanced P^(3)(1, 5)-Designs

Given a 3-uniform hypergraph H(3), an H(3)-decomposition of the complete hypergraph K(3)_v is a collection of hypergraphs, all isomorphic to H(3), whose edge sets partition the edge set of K(3)_v. An H(3)-decomposition of K(3)_v is also called an H(3)-design and the hypergraphs of the partition are said to be the blocks. An H(3)-design is said to be balanced if the number of blocks containing any given vertex of K(3)_v is a constant. In this paper, we determine completely, without exceptions, the spectrum of balanced P(3)(1 5)-designs

Drop cost and wavelength optimal two-period grooming with ratio 4

We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time, there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and C=4 and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case

Il fenomeno delle dipendenze patologiche nella Provincia di Siracusa. Anno 2005. I Rapporto

Report on the state of legal and illegal substances use in the territory of Siracusa ProvinceIl Report analizza il fenomeno delle dipendenze nel territorio della Provincia di Siracusa. La descrizione del fenomeno si sviluppa intorno all\u27analisi degli indicatori individuati dall\u27Osservatorio Europeo delle Dipendenze di Lisbona (OEDT): 1-uso di sostanze nella popolazione generale (questo indicatore va a rilevare i comportamenti nei confronti di alcol e sostanze psicoattive da parte della popolazione generale); 2-prevalenza d\u27uso problematico delle sostanze psicoattive; 3-domanda di trattamento degli utilizzatori di sostanze; 4-mortalit? degli utilizzatori di sostanze; 5-malattie infettive. Altri due importanti indicatori che si stanno sviluppando, e che vengono qui illustrati, sono l\u27analisi delle Schede di Dimissione Ospedaliera (SDO) e gli indicatori relativi alle conseguenza sociali dell\u27uso di droghe (criminalit? droga correlata). Inoltre sono state applicate diverse metodologie standard di stima sia per quantificare la quota parte sconosciuta di utilizzatori di sostanze che non afferiscono ai servizi, sia per identificarne alcune caratteristiche

Perfect dodecagon quadrangle systems

AbstractA dodecagon quadrangle is the graph consisting of two cycles: a 12-cycle (x1,x2,…,x12) and a 4-cycle (x1,x4,x7,x10). A dodecagon quadrangle system of order n and index ρ [ DQS] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint dodecagon quadrangles (called blocks) which partitions the edge set of ρKn, with vertex set X. A dodecagon quadrangle system of order n is said to be perfect [PDQS] if the collection of 4-cycles contained in the dodecagon quadrangles form a 4-cycle system of order n and index μ. In this paper we determine completely the spectrum of DQSs of index one and of PDQSs with the inside 4-cycle system of index one

Hexagon quadrangle systems

AbstractA hexagon quadrangle system of order n and index ρ [HQSρ(n)] is a pair (X,H), where X is a finite set of n vertices and H is a collection of edge disjoint hexagon quadrangles (called blocks) which partitions the edge set of ρKn, with vertex set X. A hexagon quadrangle system is said to be a 4-nesting [N(4)-HQS] if the collection of all the 4-cycles contained in the hexagon quadrangles is a ρ/2-fold 4-cycle system. It is said to be a 6-nesting [N(6)-HQS] if the collection of 6-cycles contained in the hexagon quadrangles is a (3ϱ4)-fold 6-cycle system. It is said to be a (4,6)-nesting, briefly a N(4,6)-HQS, if it is both a 4-nesting and a 6-nesting.In this paper we determine completely the spectrum of N(4,6)-HQS for λ=6h, μ=4h and ρ=8h, h positive integer

Equitable specialized block-colourings for 4-cycle systems—I

AbstractA block-colouring of a 4-cycle system (V,B) of order v=1+8k is a mapping ϕ:B→C, where C is a set of colours. Every vertex of a 4-cycle system of order v=8k+1 is contained in r=v−12=4k blocks and r is called, using the graph theoretic terminology, the degree or the repetition number. A partition of degree r into s parts defines a colouring of type s in which the blocks containing a vertex x are coloured exactly with s colours. For a vertex x and for i=1,2,…,s, let Bx,i be the set of all the blocks incident with x and coloured with the ith colour. A colouring of type s is equitable if, for every vertex x, we have |Bx,i−Bx,j|≤1, for all i,j=1,…,s. In this paper we study bicolourings, tricolourings and quadricolourings, i.e. the equitable colourings of type s with s=2, s=3 and s=4, for 4-cycle systems

Extremal gaps in BP3-designs

In this paper we examine Voloshin’s colorings of mixed hypergraphs derived from P3-designs and construct families of P3-designs having the chromatic spectrum with the leftmost hole and rightmost hole