Chvátal's conjecture and point-intersections
✍ Scribed by Peter Stein
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 256 KB
- Volume
- 43
- Category
- Article
- ISSN
- 0012-365X
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📜 SIMILAR VOLUMES
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,, be finite sers such that A,@ A, for all i \* j. Let F be an intencctlng family con&ting of sets contained in some A,. i = 1. 2. . . . n. I\_'hvital conjecl urtxl that among the largest irtersecting families. there is always a star. In Ihi\ pi per. we oNam another proof of a result of Schiinheim:
It is shown that among the maximal intersecting systems, which are subsystems of a hereditary family F, there is a star, as claimed by a conjecture of ChvBtal, if it is assumed, that the number of bases of F is n, but it -1 bases of F form a simple-star. ## 1. Mroduction V. Chv;ital [l] conjecture