## Abstract It is well known that every bipartite graph with vertex classes of size __n__ whose minimum degree is at least __n__/2 contains a perfect matching. We prove an analog of this result for hypergraphs. We also prove several related results that guarantee the existence of almost perfect mat
Matching extension and minimum degree
β Scribed by N. Ananchuen; L. Caccetta
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 495 KB
- Volume
- 170
- Category
- Article
- ISSN
- 0012-365X
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π SIMILAR VOLUMES
Let G be a graph with a perfect matching and k be an integer such that l~<k< I V(G)l/2. Then G is said to be k-extendable if every matching of size k in G extends to a perfect matching of G. Plummer (1994) proved that every (2k + 1)-connected K~,s-free graph of even order is k-extendable. In this p
We prove that in a graph of order n and minimum degree d, the mean distance Β΅ must satisfy This asymptotically confirms, and improves, a conjecture of the computer program GRAFFITI. The result is close to optimal; examples show that for any d, Β΅ may be larger than n/(d + 1).