Transversals in Rectangles
نویسنده
چکیده
Let L(m;n) be the largest integer such that, if each symbol in an m n rectangle occurs at most L(m;n) times, then the array must have a transversal. We improve the lower bound to L(m;n) b m+1) 1 m 1 c, form > 1. Then we show that sporadically L(m;n) < bmn 1 m 1 c in the range m n m 3m + 3. De ne n0(m) to be the smallest integer z such that if n z then L(m;n) = bmn 1 m 1 c. We improve n0(m) from O(m ) to O(m). Finally, we determine L(4; n) for all n.
منابع مشابه
A study of Nilpotent groups through right transversals
In group theory nilpotency of a group has a great importance. In this paper we have studied some concept of nilpotency through right transversals. We have also studied prime power groups and frattini subgroups through right transversals.
متن کاملEnumerating Minimal Transversals of Geometric Hypergraphs
We consider the problem of enumerating all minimal hitting sets of a given hypergraph (V,R), where V is a finite set, called the vertex set andR is a set of subsets of V called the hyperedges. We show that, when the hypergraph admits a balanced subdivision, then a recursive decomposition can be used to obtain efficiently all minimal hitting sets of the hypergraph. We apply this decomposition fr...
متن کاملOutput-Sensitive Algorithms for Enumerating Minimal Transversals for Some Geometric Hypergraphs
We give a general framework for the problem of finding all minimal hitting sets of a family of objects in R by another. We apply this framework to the following problems: (i) hitting hyper-rectangles by points in R; (ii) stabbing connected objects by axis-parallel hyperplanes in R; and (iii) hitting half-planes by points. For both the covering and hitting set versions, we obtain incremental pol...
متن کاملA THEORETICALLY CORRECT RESOURCE USAGE VISUALIZATION FOR THE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM
The cumulative resource constraints of the resource-constrained project scheduling problem (RCPSP) do not treat the resource demands as geometric rectangles, that is, activities are not necessarily assigned to the same resource units over their processing times. In spite of this fact, most papers on resource-constrained project scheduling mainly in the motivation phase use a strip packing of re...
متن کاملTransversals in Latin Squares: A Survey
A latin square of order n is an n×n array of n symbols in which each symbol occurs exactly once in each row and column. A transversal of such a square is a set of n entries containing no pair of entries that share the same row, column or symbol. Transversals are closely related to the notions of complete mappings and orthomorphisms in (quasi)groups, and are fundamental to the concept of mutuall...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006