Soit H = (X. ~1 un hypergraphe h-uniforme avec IX] = net soit L h ~(H! le graphe Jont les sommets reprdsentent les arates de H, deux sommets 6lant reli6s si et seulement si t~s z~r6tes qu'ils reprdsen!ent intersectent en h -1 sommet,=. Nous montrons que sif,, t(H) ne contienl pas de cycle, alors I~[
On the maximum number of edges in a hypergraph with a unique perfect matching
โ Scribed by Deepak Bal; Andrzej Dudek; Zelealem B. Yilma
- Book ID
- 113567385
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 193 KB
- Volume
- 311
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Sanchis, L.A., Maximum number of edges in connected graphs with a given domination number, Discrete Mathematics 87 (1991) 65-72.
Suppose that n i> 2t + 2 (t/> 17). Let G be a graph with n vertices such that its complement is connected and, for all distinct non-adjacent vertices u and v, there are at least t common neighbours. Then we prove that and Furthermore, the results are sharp.
A perfect matching or a l-factor of a graph G is a spanning subgraph that is regular of degree one. Hence a perfect matching is a set of independent edges which matches all the nodes of G in pairs. Thus in a hypercube parallel processor, the number of perfect matchings evaluates the number of diff