Horiik, P., Extending partial systems of distinct representatives, Discrete Mathematics 91 (1991) 95-98. We determine a necessary and sufficient condition for a special class of families of sets to have the property that each partial SDR of cardinahty d can be extended to a total SDR. This result i
Systems of distinct representatives, II
β Scribed by Phillip A Ostrand
- Publisher
- Elsevier Science
- Year
- 1970
- Tongue
- English
- Weight
- 174 KB
- Volume
- 32
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Agrawal (1966 Ann. Math. Statist. 37, 525-528) explored the concept of systems of distinct representatives to show that the treatments in a binary equireplicated incomplete block design can be rearranged within blocks such that the treatments occur as close to equally often as possible in every row.
The main result of this paper can be quickly described as follows. Let G be a bipartite graph and assume that for any vertex v of G a strongly base orderable matroid is given on the set of edges adjacent with v. Call a subgraph of G a system of representatives of G if the edge neighborhood of each v
This paper applies a recent theorem about simultaneous systems of representatives for families of finite sets to obtain combinatorial results that are closely related to problems concerning minimal asymptotic bases in additive number theory.