We investigate the relations among the chromatic index q(X), the maximum degree d(Z), the total chromatic number q\*(Z), and the maximum size d,(Z) of an intersecting subhypergraph of a hypergraph Z: For some particular classes of hypergraphs, including Steiner systems, we provide sufficient conditi
A result concerning two conjectures of Berge and Chvátal
✍ Scribed by M. Gionfriddo; S. Milici
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 142 KB
- Volume
- 155
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract Chvátal has shown that if __T__ is a tree on __n__ points then __r__(__K~k~, T__) = (__k__ – 1) (__n__ – 1) + 1, where __r__ is the (generalized) Ramsey number. It is shown that the same result holds when __T__ is replaced by many other graphs. Such a __T__ is called __k__‐good. The res
Let G be a bridgeless cubic graph. Fulkerson conjectured that there exist six 1-factors of G such that each edge of G is contained in exactly two of them. Berge conjectured that the edge-set of G can be covered with at most five 1-factors. We prove that the two conjectures are equivalent.
It is possible to find II partitions of an n-element set whose pairwise intersections are just all atoms of the partition lattice? Demetrovics, Ftiredi and Katona verified this for all n -1 or 4 (mod 12) by constructing a series of special Mendelsohn Triple Systems. They conjectured that such tripl