Showing papers in "Discrete Mathematics in 2004"

TL;DR: The graph theoretic properties of this variant of the domination number of a graph G, a function f : V→{0,1,2} satisfying the condition that every vertex u is adjacent to at least one vertex v for which f(v)=2, are studied.

TL;DR: Several new problems motivated by covering arrays applications are raised and algorithms for their solution are discussed.

TL;DR: It is proved that max {d j +m j : v j ∈V}⩽ 2e n−1 +n−2 with equality if and only if G is an Sn graph (K1,n−1 ⊆Sn⊆Kn) or a complete graph of order n− 1 with one isolated vertex.

TL;DR: Using the hull dimension spectra of linear codes, it is shown that linear codes with complementary dual meet the asymptotic Gilbert-Varshamov bound.

TL;DR: Confirming non-rigorous arguments of Dorogovtsev et al. and Drinea et al., this shows that for such a, the proportion P(d) of vertices of degree d almost surely obeys a power law, where P( d) is of the form d-^2^-^a for large d.

TL;DR: Three methods, a numerical, a geometric and an algebraic one are proposed to automate also this last step of automated deduction of previous conjectures, strengthening of a series of conjectures from Graffiti and obtention of several new conjectures.

TL;DR: This paper introduces a generalization of cover-free families which includes as special cases all of the previously used definitions, and gives several bounds and some efficient constructions for these generalized cover- free families.

TL;DR: This work considers the properties of certain graphs based on iteration of the quadratic maps x->x^2 and x-> x^2-2 over a finite field GF(p).

TL;DR: Some upper and lower bounds on the greatest eigenvalue and a lower bound on the smallest eigen value are presented.

TL;DR: In this article, the authors introduce cooperative games with a feasible coalition system called antimatroid, which is a combinatorial structure generalizing the permission structures, and characterize the approaches from a permission structure with special classes of antimatroids.

TL;DR: A combinatorial form of the Kadison–Singer problem, a famous problem in C ∗ -algebra, is given, which has several minor variations and some partial results can be easily deduced from known facts in discrepancy theory.

TL;DR: This paper reviews foundational, historical, and philosophical issues of crossing numbers, and shows a new lower bound for crossing numbers that may be helpful in estimating crossing numbers.

TL;DR: For each class, a lower bound on the size of matchings is given, and it is shown that the bound is tight for some graph within the class.

TL;DR: This paper introduces three new types of combinatorial designs, which they are called external difference families (EDF), external BIBDs (EBIBD) and splitting BIBD, and proves a weak converse, showing that if there exist an optimal secret sharing scheme, then there exists an EBIBD.

TL;DR: It is shown that if G is a polygon-circle graph, then so is [ L ( G )] 2 , and the same holds for asteroidal triple-free and interval-filament graphs, and it follows that the induced matching problem is polytime-solvable in these classes.

TL;DR: The rainbow numbers rb(n,K"k) for all n>=k>=4, and the rainbowNumbers rb (n,kK"2) forall k>=2 and n> =3k+3 are determined.

TL;DR: This note shows that p ¯ ( n ) ≡ 0 ( mod 64 ) for a set of integers of arithmetic density 1.

TL;DR: The distinguishing number of a graph G is the minimum number of colors for which there exists an assignment of colors to the vertices of G so that the group of color-preserving automorphisms of G consists only of the identity.

TL;DR: Considering a linearly ordered set, its symmetric version is introduced, and endow it with two operations extending supremum and infimum, so as to obtain an algebraic structure close to a commutative ring.

TL;DR: The spectrum for {4}-GDDs of type gum1 is established, up to a finite number of values of u, where gu is even, g ∉ {11, 17}.

TL;DR: The aim of this paper is to draw the attention of the marketers to the potential of netnography by giving it a rigorous theoretical framework, and by proposing some helps for its implementation.

TL;DR: Given a positive integer n and a family F of graphs, let R^*(n,F) denote the maximum number of colors in an edge-coloring of K"n such that no subgraph of K'n belonging to F has distinct colors on its edges.

TL;DR: The computational complexity of finding the forcing number of graphs is studied, and some results on the possible values of forcing number for different matchings of the hypercube Q(n) are given.

TL;DR: This paper studies L (2,1)-labeling numbers of Cartesian products of paths and cycles of a graph G, which is the minimum cardinality k such that G has a k - L ( 2,1-labeling.

TL;DR: It is proved that, with the exception of the Gray graph on 54 vertices, every cubic edge- transitive graph of order 2p^3 is vertex-transitive.

TL;DR: It is proved that there exists a cyclic Hamiltonian k-cycle system of the complete graph if and only if k is odd but k≠15 and pα with p prime and α>1.

TL;DR: The signed total domination number of G is the minimum weight of a signed total dominating function (STDF) of G, while the upper signed total dominates number ofG is the maximum weight ofA minimal STDF on G.

TL;DR: This work combines two topics in directed graphs, vertex pushing and homomorphisms, by studying homomorphicisms of equivalence classes of oriented graphs under the push operation, and it is proved that the pushable chromatic number of a partial 2-tree is at most four.

TL;DR: For all r, the exact value of the best possible density of an r-identifying code in the king lattice is given, i.e., the infinite two-dimensional square lattice with two diagonals.

TL;DR: The statistic “number of udu 's” in Dyck paths is considered and its generating functions, their recurrence relations and their explicit formulas are derived.