We present a conjecture, with some supporting results, concerning the maximum size of a family of subsets satisfying the following conditions: the intersection of any two members of the family has cardinal@ at least s, and the intersection of the complements of any two members has cardinal@ at least
β¦ LIBER β¦
Tight bounds on a problem of lines and intersections
β Scribed by Micha Sharir; Steven S. Skiena
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 100 KB
- Volume
- 89
- Category
- Article
- ISSN
- 0012-365X
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It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It