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Hamilton decompositions of complete 3-uniform hypergraphs

✍ Scribed by Helen Verrall

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
947 KB
Volume
132
Category
Article
ISSN
0012-365X

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✦ Synopsis

The problem of finding a Hamilton decomposition of the complete 3-uniform hypergraph K,3 has been solved for n = 2 (mod 3) and n = 4(mod 6) . We find here a Hamilton decomposition of Ki, no l(mod 6), and a Hamilton decomposition of the complete 3-uniform hypergraph minus a l-factor, Ki -I, n = 0 (mod 3), and thereby complete the problem. A hypergraph X'( V, 8) is a set of vertices P'= V(2)= { 1,2, . . . , n} and a set of hyperedges ~=~(LW)={E,,E~,... ,E,}, where Ei~ V and IEi)>O, l<ibm. If 1 Eil = h, we call Ei an h-edge. If 1 Ei( = h, for all EiE&', then we call # h-unifbrm. The complete h-uniform hypergraph on n vertices, denoted Ki, is a hypergraph on the n vertices of V, in which every h-subset of V determines a hyperedge, or h-edge. It

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