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Combinatorial aspects of covering arrays
 Le Matematiche (Catania
"... Covering arrays generalize orthogonal arrays by requiring that ttuples be covered, but not requiring that the appearance of ttuples be balanced. Their uses in screening experiments has found application in software testing, hardware testing, and a variety of fields in which interactions among fact ..."
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Cited by 34 (8 self)
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Covering arrays generalize orthogonal arrays by requiring that ttuples be covered, but not requiring that the appearance of ttuples be balanced. Their uses in screening experiments has found application in software testing, hardware testing, and a variety of fields in which interactions among factors are to be identified. Here a combinatorial view of covering arrays is adopted, encompassing basic bounds, direct constructions, recursive constructions, algorithmic methods, and applications.
Octagon Quadrangle Systems nesting 4kitedesigns having equiindices
"... An octagon quadrangle is the graph consisting of an 8cycle (x1,..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS] is a pair (X, B), where X is a finite set of v vertices and B is a collection of edge disjoint octagon quadr ..."
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An octagon quadrangle is the graph consisting of an 8cycle (x1,..., x8) with two additional chords: the edges {x1, x4} and {x5, x8}. An octagon quadrangle system of order v and index λ [OQS] is a pair (X, B), where X is a finite set of v vertices and B is a collection of edge disjoint octagon quadrangles (called blocks) which partition the edge set of λKv defined on X. A 4kite is the graph having five vertices x1, x2, x3, x4, y and consisting of an 4cycle (x1, x2,..., x4) and an additional edge {x1, y}. A 4kite design of order n and index µ is a pair K = (Y, H), where Y is a finite set of n vertices and H is a collection of edge disjoint 4kite which partition the edge set of µKn defined on Y. An Octagon Kite System [OKS] of order v and indices (λ, µ) is an OQS(v) of index λ in which it is possible to divide every block in two 4kites so that an 4kite design of order v and index µ is defined. In this paper we determine the spectrum for OKS(v) nesting 4kitedesigns of equiindices (2,3). Lavoro eseguito nell’ambito del progetto PRIN 2008: Disegni Combinatorici, Grafi e loro applicazioni.
On the Upper Chromatic Number of a Hypergraph
, 1995
"... We introduce the notion of a coedge of a hypergraph, which is a subset of vertices to be colored so that at least two vertices are of the same color. Hypergraphs with both edges and coedges are called mixed hypergraphs. The maximal number of colors for which there exists a mixed hypergraph colorin ..."
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Cited by 27 (8 self)
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We introduce the notion of a coedge of a hypergraph, which is a subset of vertices to be colored so that at least two vertices are of the same color. Hypergraphs with both edges and coedges are called mixed hypergraphs. The maximal number of colors for which there exists a mixed hypergraph coloring using all the colors is called the upper chromatic number of a hypergraph H and is denoted by (H). An algorithm for computing the number of colorings of a mixed hypergraph is proposed. The properties of the upper chromatic number and the colorings of some classes of hypergraphs are discussed. A greedy polynomial time algorithm for finding a lower bound for (H) of a hypergraph H containing only coedges is presented.
Uniform Coloured Hypergraphs and Blocking Sets
, 2013
"... In this paper some properties of kchromatic and strong kchromatic hypergraphs are proved. Conditions for the possible existence of blocking sets in Steiner systems are established. ..."
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In this paper some properties of kchromatic and strong kchromatic hypergraphs are proved. Conditions for the possible existence of blocking sets in Steiner systems are established.
An edge colouring of multigraphs
 COMPUTER SCIENCE JOURNAL OF MOLDOVA, VOL.15, NO.2(44)
, 2007
"... We consider a strict kcolouring of a multigraph G as a surjection f from the vertex set of G into a set of colours {1,2,...,k} such that, for every nonpendant vertex x of G, there exist at least two edges incident to x and coloured by the same colour. The maximum number of colours in a strict edge ..."
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Cited by 1 (0 self)
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We consider a strict kcolouring of a multigraph G as a surjection f from the vertex set of G into a set of colours {1,2,...,k} such that, for every nonpendant vertex x of G, there exist at least two edges incident to x and coloured by the same colour. The maximum number of colours in a strict edge colouring of G is called the upper chromatic index of G and is denoted by χ(G). In this paper we prove some results about it.
On the Upper Chromatic Index of a Multigraph
 Computer Science Journal of Moldova
, 2001
"... We consider the colorings of the edges of a multigraph in such a way that every nonpendant vertex is incident to at least two edges of the same color. We prove that the upper chromatic index is equal to c+mn+p where c is the maximum number of vertex disjoint cycles, m,n and p are the numbers of ed ..."
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Cited by 5 (2 self)
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We consider the colorings of the edges of a multigraph in such a way that every nonpendant vertex is incident to at least two edges of the same color. We prove that the upper chromatic index is equal to c+mn+p where c is the maximum number of vertex disjoint cycles, m,n and p are the numbers of edges, vertices and pendant vertices of a multigraph.
Perfect octagon quadrangle systems with upper C4systems
 Berardi, Mario Gionfriddo, Rosaria Rota
"... upper C4system and a large spectrum ∗ ..."
Lower and upper chromatic numbers for BSTSs(2 h 1)
, 2001
"... In [Discrete Math. 174, (1997) 247259] an infinite class of STSs(2h −1) was found with the upper chromatic number ¯χ = h. We prove that in this class, for all STSs(2h − 1) with h < 10, the lower chromatic number coincides with the upper chromatic number, i.e. χ = ¯χ = h; and moreover, there exis ..."
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In [Discrete Math. 174, (1997) 247259] an infinite class of STSs(2h −1) was found with the upper chromatic number ¯χ = h. We prove that in this class, for all STSs(2h − 1) with h < 10, the lower chromatic number coincides with the upper chromatic number, i.e. χ = ¯χ = h; and moreover, there exists a infinite subclass of STSs with χ = ¯χ = h for any value of h.
Results 1  10
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24