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Families close to disjoint ones

✍ Scribed by P. Komjáth

Book ID
105413966
Publisher
Akadmiai Kiad
Year
1984
Tongue
English
Weight
553 KB
Volume
43
Category
Article
ISSN
1588-2632

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📜 SIMILAR VOLUMES

Drawings of Cm×Cn with One Disjoint Fami
Drawings of Cm×Cn with One Disjoint Family
✍ Gelasio Salazar 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 102 KB

We show that every drawing of C m \_C n with either the m n-cycles pairwise disjoint or the n m-cycles pairwise disjoint has at least (m&2) n crossings, for every m, n satisfying n m 3. This supports the long standing conjecture by Harary et al. that the crossing number of C m \_C n is (m&2) n.

On Union-Closed Families, I
On Union-Closed Families, I
✍ Robert T. Johnson; Theresa P. Vaughan 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 174 KB

A union closed family A is a finite family of sets such that the union of any two sets in A is also in A. The conjecture under consideration is Conjecture 1: For every union closed family A, there exists some x contained in at least half the members of A. We study the structure of such families (as

On Union-Closed Families, I
On Union-Closed Families, I
✍ Robert T. Johnson; Theresa P. Vaughan 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 93 KB
Drawings of Cm×Cn with One Disjoint Fami
Drawings of Cm×Cn with One Disjoint Family II
✍ Hector A. Juarez; Gelasio Salazar 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 99 KB

A long-standing conjecture states that the crossing number of the Cartesian product of cycles C m \_C n is (m&2) n, for every m, n satisfying n m 3. A crossing is proper if it occurs between edges in different principal cycles. In this paper drawings of C m \_C n with the principal n-cycles pairwise