منابع مشابه
More on Decomposing Coverings by Octants
In this note we improve our upper bound given in [7] by showing that every 9-fold covering of a point set in R by finitely many translates of an octant decomposes into two coverings, and our lower bound by a construction for a 4-fold covering that does not decompose into two coverings. We also prove that certain dynamic interval coloring problems are equivalent to the above question. The same b...
متن کاملDecomposition of multiple coverings into more parts
We prove that for every centrally symmetric convex polygonQ, there exists a constant α such that any locally finite αk-fold covering of the plane by translates of Q can be decomposed into k coverings. This improves on a quadratic upper bound proved by Pach and Tóth. The question is motivated by a sensor network problem, in which a region has to be monitored by sensors with limited battery life.
متن کاملInformation Hiding by Coverings *
We propose a formal model for embedding information in black-white images and prove the equivalence between existence of embedding schemes and covering codes. An asymptoticly tight bound on the performance of embedding schemes is given. We construct efficient embedding schemes via known coverings. In particular, one of those schemes allows to embed up to log 2 (n + 1) bits in coverwords of n bi...
متن کاملTolerances Induced by Irredundant Coverings
In this paper, we consider tolerances induced by irredundant coverings. Each tolerance R on U determines a quasiorder .R by setting x .R y if and only if R(x) ⊆ R(y). We prove that for a tolerance R induced by a covering H of U , the covering H is irredundant if and only if the quasiordered set (U,.R) is bounded by minimal elements and the tolerance R coincides with the product &R ◦.R. We also ...
متن کاملMultiple vertex coverings by cliques
For positive integers m1, . . . ,mk, let f(m1, . . . ,mk) be the minimum order of a graph whose edges can be coloured with k colours such that every vertex is in a clique of cardinality mi all of whose edges have the i th colour for all i = 1, 2, . . . , k. The value for k = 2 was determined by Entringer et al. (J. Graph Theory 24 (1997), 21–23). We show that if k is fixed then f(m, . . . ,m) =...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1984
ISSN: 0097-3165
DOI: 10.1016/0097-3165(84)90010-4