## 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
Quadrangular embeddings of the complete even k-partite graph
β Scribed by Nora Hartsfield; Gerhard Ringel
- Publisher
- Elsevier Science
- Year
- 1990
- Tongue
- English
- Weight
- 240 KB
- Volume
- 81
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
The complete even k-partite graph K n,.n* ,..., "* is the complete k-partite graph where all the n,'s are even numbers. Orientable and nonorientable quadrangular embeddings are constructed for all these graphs.
π SIMILAR VOLUMES
## Abstract We prove that for every prime number __p__ and odd __m__>1, as __s__ββ, there are at least __w__ face 2βcolorable triangular embeddings of __K__~__w, w, w__~, where __w__ = __m__Β·__p__^__s__^. For both orientable and nonorientable embeddings, this result implies that for infinitely many
A generalization of a recent result of Tomescu ( 1993) is presented. The method is purely combinatorial and is based on the theory of species of several variables.
A graph is constructed to provide a negative answer to the following question of Bondy: Does every diconnected orientation of a complete k-partite (k 2 5) graph with each part of size at least 2 yield a directed (k + 1)-cycle?
## Abstract Graham and Pollak [3] proved that __n__ β1 is the minimum number of edgeβdisjoint complete bipartite subgraphs into which the edges of __K__~__n__~ can be decomposed. Using a linear algebraic technique, Tverberg [2] gives a different proof of that result. We apply his technique to show