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On maximal antichains consisting of sets and their complements

✍ Scribed by Hans-Dietrich O.F Gronau


Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
320 KB
Volume
29
Category
Article
ISSN
0097-3165

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πŸ“œ SIMILAR VOLUMES


On maximal antichains containing no set
✍ G.F. Clements; H.-D.O.F. Gronau πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 1016 KB

Let 16k,dk,+.. d k,, be integers and let S denote the set of all vectors x =(x1, . . . , x,) with integral coordinates sz@@ing 05% "4, i = 1,2, . . . r n; equivalently, .S is the set of ail subset of' a mtitiset eonsistiitg of & elements of type i, i = 1,2,. . . , n. A subset X of 3" is an antichain

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We show that the necessary condition m ≀ k ≀ 3m -1 that there exists a maximal set of k triangle-factors on 6m β‰₯ 18 vertices is also sufficient, except possibly when k = m.

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We show that the necessary condition m + 1 ≀ k ≀ 3m + 1 that there exist a maximal set of k triangle-factors on 6m + 3 β‰₯ 15 vertices is also sufficient, except possibly when k = m + 1, or when 6m + 3 {45, 57, 69, 81, 93, 237, 261, 309, 333, 381}.