Journal ArticleDOI
Coin-Weighing Problems
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TLDR
In this article, coin-weighing problems are considered in the context of coin-weighting problems, and the authors propose a solution to the problem of coin weighting.Abstract:
(1995). Coin-Weighing Problems. The American Mathematical Monthly: Vol. 102, No. 2, pp. 164-167.read more
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On the Metric Dimension of Cartesian Products of Graphs
Jose´ Ca´ceres,Carmen Hernando,Merce grave,Mora,Ignacio M. Pelayo,María Luz Puertas,Carlos Seara,David R. Wood +7 more
TL;DR: It is proved that the metric dimension of G\,\square\,G$ is tied in a strong sense to the minimum order of a so-called doubly resolving set in $G$.
Journal ArticleDOI
On the Metric Dimension of Cartesian Products of Graphs
José Cáceres,Carmen Hernando,Mercè Mora,Ignacio M. Pelayo,María Luz Puertas,Carlos Seara,David R. Wood +6 more
TL;DR: In this paper, it was shown that the metric dimension of G*G is tied in a strong sense to the minimum order of a so-called doubly resolving set in G. The metric dimension is the minimum cardinality of a resolving set of G.
Journal ArticleDOI
Extremal graph theory for metric dimension and diameter
TL;DR: In this paper, it was shown that the minimum order of a graph in the set of graphs with metric dimension β and diameter β + D is exactly β+D for all values of β and D.
Journal ArticleDOI
Extremal Graph Theory for Metric Dimension and Diameter
TL;DR: In this paper, the authors characterize the graphs in Gβ,D with order β+D for all values of β and D. The first contribution is to determine the maximum order of a graph in G β,D.
Journal ArticleDOI
Anti-Hadamard Matrices, Coin Weighing, Threshold Gates, and Indecomposable Hypergraphs
Noga Alon,Văn H Vũ +1 more
TL;DR: The maximum possible absolute value of an entry of the inverse of annbyninvertible matrix with 0,1 entries is proved and the maximum possible degree of a regular multi-hypergraph onnvertices that contains no proper regular nonempty subhypergraph is shown.
References
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Journal ArticleDOI
A Combinatory Detection Problem
Staffan Söderberg,H. S. Shapiro +1 more
TL;DR: In this paper, a combinatorial detection problem is considered in the context of the Combinatory Detection Problem (CDP) and it is shown that the problem is NP-hard.
Journal ArticleDOI
On Hotelling's Weighing Problem
TL;DR: In this article, the authors considered the chemical balance problem and the spring balance problem with bias and provided designs for a balance which has a bias and for one which has no bias.
Journal ArticleDOI
On a Combinatorial Problem in Number Theory
TL;DR: In this article, the authors consider the problem of detecting a set of vectors with an integer k ≤ 2 and a finite set M of rational integers, and they show that the detection set of {v1, v2, v3, v4, v5, v6, vn} is a detecting set.
Journal ArticleDOI
Determination of a subset from certain combinatorial properties
David G. Cantor,W. H. Mills +1 more
TL;DR: In this paper, it was shown that a determining collection of 2 -1 subsets exists for n = 2~k, which implies that D(n) < n log 4/log n + O(n(\\og n)~ log log n).