In this article we define a perfect set of Euler tours of K 2k + I, I a 1-factor of K 2k , to be a set of Euler tours of K 2k + I that partition the 2-paths of K 2k , with the added condition that if ab β I, then each Euler tour contains either the digon a b a or b a b. We prove for all k > 1 that K
A Construction of a perfect set of Euler tours of K2k+1
β Scribed by K. Heinrich; H. Verrall
- Publisher
- John Wiley and Sons
- Year
- 1997
- Tongue
- English
- Weight
- 190 KB
- Volume
- 5
- Category
- Article
- ISSN
- 1063-8539
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β¦ Synopsis
In this article we prove Kotzig's Conjecture by constructing a perfect set of Euler tours of K 2 k+ 1 . As a corollary, we deduce that L(K 2 k+ 1 ), the line graph of K 2 k+ 1 , has a Hamilton decomposition.
π SIMILAR VOLUMES
The present paper describes an algorithm for constructing families of k-independent subsets & of {1,2, . . . , n} with &I >2ck", where c, = d/(k -1)2& and d is a certain constant. The algorithm has a polynomial complexity with respect to the size of the family constructed.
## Abstract A starter derived even starter that induces a perfect oneβfactorization of __K__~52~ is presented. This is the smallest order for which a perfect oneβfactorization was not previously known and is the first new βsmallβ order for which a perfect oneβfactorization has been found in nearly