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On conjectures of Berge and Chvátal

✍ Scribed by Mario Gionfriddo; Zsolt Tuza

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
533 KB
Volume
124
Category
Article
ISSN
0012-365X

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✦ Synopsis

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 conditions insuring that some (or all) of the trivial inequalities

A(~)~do(~)~q(Jro)~q*(~)

turn to equality. For instance, we prove that d(.#')=d,(Z) holds whenever the maximum degree of a hypergraph .% is sufficiently large with respect to the rank and the 'pair-degree' of Z.

📜 SIMILAR VOLUMES

Some results about the Chvátal conjectur
Some results about the Chvátal conjecture
✍ Da-Lun Wang; Ping Wang 📂 Article 📅 1978 🏛 Elsevier Science 🌐 English ⚖ 713 KB

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:

On chvátal's conjecture related to a her
On chvátal's conjecture related to a hereditary system
✍ Peter Stein 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 800 KB

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