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
On maximal antichains consisting of sets and their complements
β Scribed by Hans-Dietrich O.F Gronau
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 320 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0097-3165
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper the authors study the edge-integrity of graphs. Edge-integrity is a very useful measure of the vulnerability of a network, in particular a communication network, to disruption through the deletion of edges. A number of problems are examined, including some Nordhaus-Gaddum type results.
We show that the necessary condition m β€ k β€ 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.
We show that the necessary condition m + 1 β€ k β€ 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}.