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.
On the structure of complete graphs without alternating cycles
β Scribed by C.C. Chen
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 139 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A graph G is called k-choosable if k is a number such that if we give lists of k colors to each vertex of G there is a vertex coloring of G where each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosa
## 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 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
## Abstract Define the partial join of two graphs to be some graph arising from their disjoint union by adding a set of new edges each joining a vertex of the first graph and a vertex of the second one. We characterize all colourβcritical graphs being partial joins of a complete graph and an odd cy
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.