## Abstract In this article, it is proved that for each even integer __m__β©Ύ4 and each admissible value __n__ with __n__>2__m__, there exists a cyclic __m__βcycle system of __K__~__n__~, which almost resolves the existence problem for cyclic __m__βcycle systems of __K__~__n__~ with __m__ even. Β© 201
Cycle systems of the line graph of the complete graph
β Scribed by Cox, B.A.; Rodger, C.A.
- Publisher
- John Wiley and Sons
- Year
- 1996
- Tongue
- English
- Weight
- 562 KB
- Volume
- 21
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
For all m = 0 (mod 41, for all n = 0 or 2 (mod m), and for all n = 1 (mod 2m) w e find an m-cycle decomposition of the line graph of the complete graph K,. In particular, this solves the existence problem when m is a power of two.
π SIMILAR VOLUMES
## Abstract We construct a new symmetric Hamilton cycle decomposition of the complete graph __K~n~__ for odd __n__β>β7. Β© 2003 Wiley Periodicals, Inc.
## Abstract A 1βfactorization is constructed for the line graph of the complete graph __K~n~__ when __n__ is congruent to 0 or 1 modulo 4.
## Abstract Let __G__ be a connected graph with edge set __E__ embedded in the surface β. Let __G__Β° denote the geometric dual of __G__. For a subset __d__ of __E__, let Ο__d__ denote the edges of __G__Β° that are dual to those edges of __G__ in __d__. We prove the following generalizations of wellβ
In this paper we find the maximum number of pairwise edgedisjoint m-cycles which exist in a complete graph with n vertices, for all values of n and m with 3 β€ m β€ n.