An extension of the Kruskal-Katona theorem to colored hypergraphs was given by Frankl, Fiiredi and Kalai in [Shadows of colored complexes, Mathematics Scandinavica]. Here we give a new simple proof.
A new short proof for the Kruskal-Katona theorem
β Scribed by P Frankl
- Publisher
- Elsevier Science
- Year
- 1984
- Tongue
- English
- Weight
- 96 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
We give a very short proof for the Kruskal-Katona theorem and Lovhsz's version of it: given (~) k-element sets there are at least (k~_l) (k -1)-element sets which are contained in at least one of the k-sets.
π SIMILAR VOLUMES
We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG(n, 2) ordered by inclusion. For given k, (k < ) and m the problem is to find a family of size m in the set of -subspaces of PG(n, 2), containing the minimal number of k-subspaces. We introduce two lexicogr
## Abstract For a simple graph of maximum degree Ξ, it is always possible to color the edges with Ξ + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Ξ colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these re
Gallai and Milgram (1960) proved that a digraph with stability number ct is spanned by ct disjoint directed paths. Chen and Manalastas Jr (1983) proved that a strong digraph with stability number at most two is spanned by at most two consistent directed circuits. We slightly simplify the proof of