✦ LIBER ✦

The crossing number of K1,3,n and K2,3,n

✍ Scribed by Kouhei Asano

Publisher: John Wiley and Sons
Year: 1986
Tongue: English
Weight: 234 KB
Volume: 10
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190100102

No coin nor oath required. For personal study only.

✦ Synopsis

In this article, we will determine the crossing number of the complete tripartite graphs K,.3.n and K2,3.n. Our proof depends on Kleitman's results for the complete bipartite graphs [D. J. Kleitman, The crossing number of K5,n. J. Combhatorial Theory 9 (1970) 375-3231. a graph G is the minimum number among good immersions.

The crossing numbers of the complete bipartite graphs K,,,n were computed by D. J. Kleitman [l], for the case m 5 6. More precisely, he proved that

cr(Km,J = [ i m ] [ f ( ml ) ] [ i n ] [ i ( nl)]

, if m 5 6 .

📜 SIMILAR VOLUMES

On Integers of the Forms k−2n and k2n+1

✍ Yong-Gao Chen 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 85 KB

In this paper we prove that the set of positive odd integers k such that k&2 n has at least three distinct prime factors for all positive integers n contains an infinite arithmetic progression. The same result corresponding to k2 n +1 is also true.

The crossing number ofK3,n in a surface

✍ Richter, R. Bruce; ?ir�?, J. 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 174 KB

In this article, w e show that the crossing number of K3," in a surface with Euler genus . This generalizes a result of Guy and Jenkyns, who obtained this result for the torus. 0

Sythesis and Structure of K3N.

✍ D. Fischer; Z. Cancarevic; J. C. Schoen; M. Jansen 📂 Article 📅 2004 🏛 John Wiley and Sons ⚖ 52 KB

Iteration of the number-theoretic functi

Iteration of the number-theoretic function f(2n) = n, f(2n + 1) = 3n + 2

✍ C.J Everett 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 162 KB

Off-diagonal and asymptotic results on t

Off-diagonal and asymptotic results on the Ramsey number r(K2,m,K2,n)

✍ Roland Lortz; Ingrid Mengersen 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 210 KB 👁 1 views

## Abstract An upper bound on the Ramsey number __r__(__K__~2,__n‐s__~,__K__~2,__n__~) where __s__ ≥ 2 is presented. Considering certain __r__(__K__~2,__n‐s__~,__K__~2,__n__~)‐colorings obtained from strongly regular graphs, we additionally prove that this bound matches the exact value of __r__(__K

Barium, Potassium, and Tris(ethane-1,2-d

Barium, Potassium, and Tris(ethane-1,2-diamine)nickel(II) Fluoroalkanedisulfonates and the X-ray Crystal Structures of K2(O3S)2CHF, K2(O3S)2CF2, K2(O3S)2(CF2)3 · H2O, and [Nien3][(O3S)2(CF2)n] (n = 1, 3)

✍ Carmel T. Abrahams; Rachel Blackshaw; Glen B. Deacon; Bryan M. Gatehouse; Gerald 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 German ⚖ 215 KB 👁 3 views

The barium perfluoroalkanedisulfonates Ba(O 3 S) 2 (CF 2 ) n (n = 1, 3±5) and the new potassium fluoroalkanedisulfonates K 2 (O 3 S) 2 CHF, K 2 (O 3 S) 2 CF 2 , and K 2 (O 3 S) 2 (CF 2 ) 5 have been prepared by reaction of (CF 2 ) n (SO 2 F) 2 (n = 1, 3±5) or CHF(SO 2 F) 2 with CaO (or Ca(OH) 2 ) an