R. Ahlswede and N.Cai, On extremal set partitions in Cartesian product spaces, Combinatorics, Probability and Computing 2, 211-220, 1993. Home/Search Document Details and Download
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Matching Numbers for n-th Powers of Bipartite Graphs and.. - Althöfer (1999) (Correct)
....of arbitrary graphs and found a well characterized function which bounds the capacity and equals the capacity in a large number of cases. He obtained several results on the capacity of special graphs. In 1993 Ahlswede and Cai investigated extremal set partitions in Cartesian product spaces in [1]. For a given hypergraph H = V; E) where V is a finite set of vertices and E a system of subsets (hyperedges) of V, and products of hypergraphs they analyzed packing numbers (that is the maximal size of a disjoint hyperedge set in a given hypergraph) covering numbers (that is the minimal ....
.... disjoint hyperedge set in a given hypergraph) covering numbers (that is the minimal number of hyperedges to cover all vertices in a given hypergraph) and partition numbers (that is the minimal size of a vertex partition of a given graph into edge sets) Let us cite one remarkable opinion given in [1]: It seems to us that an understanding of these partition problems would be a significant contribution to an understanding of the basic, and seemingly simple, notion of Cartesian products. Partitioning and packing products with rectangles was discussed in [2] only one year later. Here Ahlswede ....
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R. Ahlswede and N.Cai, On extremal set partitions in Cartesian product spaces, Combinatorics, Probability and Computing 2, 211-220, 1993.
Information and Control: Matching Channels - Ahlswede, Cai (1995) (1 citation) Self-citation (Ahlswede Cai) (Correct)
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R. Ahlswede and N. Cai, "On extremal set partitions in Cartesian product spaces", Combinatorics, Probability & Computing 2, 211--220, 1993.
On Partitioning And Packing Products With Rectangles - Ahlswede, Cai (1994) (1 citation) Self-citation (Ahlswede Cai) (Correct)
.... PARTITIONING AND PACKING PRODUCTS WITH RECTANGLES Rudolf Ahlswede and Ning Cai Universit at Bielefeld Fakult at f ur Mathematik Postfach 100131 33501 Bielefeld Germany Abstract In [1] we introduced and studied for product hypergraphs H n = Q n i=1 H i , where H i = V i ; E i ) the minimal size (H n ) of a partition of V n = Q n i=1 V i into sets that are elements of E n = Q n i=1 E i . The main result was that (H n ) n Y i=1 (H i ) 1) if the H i ....
....2 f1; dg for all E 2 E : In particular there are d uniform hypergraphs with all loops included, that is, Phi fvg : v 2 V Psi ae E . When the set Gamma V d Delta of all vertex sets of cardinality d is contained in the edge set E , then we speak of a complete d uniform hypergraph. In [1] we introduced the partition number (H) as the minimal size of a partition of V into sets that are members of E , if a partition exists, and as 1 otherwise. When G i = V i ; E i ) i = 1; 2; n) are arbitrary finite graphs with all loops included, then we have obviously for the ....
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R. Ahlswede and N. Cai, On extremal set partitions in Cartesian product spaces, Combinatorics, Probability & Computing 2, 211--220, 1993.
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