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The genus of Kn − K2

✍ Scribed by Mark Jungerman

Publisher
Elsevier Science
Year
1975
Tongue
English
Weight
324 KB
Volume
18
Category
Article
ISSN
0095-8956

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📜 SIMILAR VOLUMES

On the genus of the graph Kn × K2 or the
On the genus of the graph Kn × K2 or the n-prism
✍ Gerhard Ringel 📂 Article 📅 1977 🏛 Elsevier Science 🌐 English ⚖ 591 KB

For all n $ S or 9 (mod 12) the genu3 :lf the granh II, x K, is shown t#c> be equal to the lower hound given by the Euler Formula. Consider two disjoint copies of a complete graph K,, the first t&h vertices 1,2, . . -, n, the second with vertices l', 2', . . .) n'. Then join vertex i with vertex i'

A nonorientable triangular embedding of
A nonorientable triangular embedding of Kn − K2, n ≡ 8 (mod 12)
✍ Vladimir P. Korzhik 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 548 KB

The problem of construction of a nonorientable triangular embedding of the graph K, -K 2, n -8(rood 12), n >/ 1, was posed in the course of the proof of the Map Colour Theorem, but it remained an open problem. In this paper the embedding is constructed.

The genus 2 crossing number of K9
The genus 2 crossing number of K9
✍ Adrian Riskin 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 716 KB

Our main result is that a 1971 conjecture due to Paul Kainen is false. Kainen's conjecture implies that the genus 2 crossing number of K 9 is 3. We disprove the conjecture by showing that the actual value is 4. The method used is a new one in the study of crossing numbers, involving proof of the imp

Cyclic k-cycle systems of order 2kn + k:
Cyclic k-cycle systems of order 2kn + k: A solution of the last open cases
✍ Andrea Vietri 📂 Article 📅 2004 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB

## Abstract We exhibit cyclic (__K~v~__, __C~k~__)‐designs with __v__ > __k__, __v__ ≡ __k__ (mod 2__k__), for __k__ an odd prime power but not a prime, and for __k__ = 15. Such values were the only ones not to be analyzed yet, under the hypothesis __v__ ≡ __k__ (mod 2__k__). Our construction avail