𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Great intersecting families of edges in hereditary hypergraphs

✍ Scribed by D Miklós

Publisher
Elsevier Science
Year
1984
Tongue
English
Weight
250 KB
Volume
48
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

the following conjecture: If Y~ is a hereditary hypergraph on S and .gCcy~ is a family of maximum cardinality of pairwise intersecting members of ~, then there exists an xeS such that d~(x)=l{HeYe:xeH}l=l.al. Berge and Schrnheim proved that 1~1~½ I~el for every ~ and ~. Now we prove that if there exists an .~, I~1 = [½ I~el] then Chvfital's conjecture is true for this ~.

📜 SIMILAR VOLUMES

Edge search in graphs and hypergraphs of
Edge search in graphs and hypergraphs of bounded rank
✍ Ingo Althöfer; Eberhard Triesch 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 512 KB

Althofer, 1. and E. Triesch, Edge search in graphs and hypergraphs of bounded rank, Discrete Mathematics 115 (1993) l-9.

Fractional v. Integral Covers in Hypergr
Fractional v. Integral Covers in Hypergraphs of Bounded Edge Size
✍ Jeff Kahn; P.Mark Kayll 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 470 KB

In the early 1980's, V. Ro dl proved the Erdo s Hanani Conjecture, sparking a remarkable sequence of developments in the theory of packing and covering in hypergraphs of bounded edge size. Generalizations were given by P. Frankl and Ro dl, by N. Pippenger, and by others. In each case, an appropriate

On the Number of Edges in Hypergraphs Cr
On the Number of Edges in Hypergraphs Critical with Respect to Strong Colourings
✍ Alexandr V. Kostochka; Douglas R. Woodall 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 94 KB

A colouring of the vertices of a hypergraph G is called strong if, for every edge A, the colours of all vertices in A are distinct. It corresponds to a colouring of the generated graph (G) obtained from G by replacing every edge by a clique. We estimate the minimum number of edges possible in a k-cr

On the use of alternating chains and hyp
On the use of alternating chains and hypergraphs in edge coloring
✍ D. de Werra 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 320 KB

## Abstract Existence of some generalized edge colorings is proved by using the properties of hypergraphs as well as alternating chain methods. A general framework is given for edge colorings and some general properties of balancing are derived.