Constructing Homogeneous Factorisations of Complete Graphs and Digraphs
β Scribed by Cai Heng Li; Cheryl E. Praeger
- Book ID
- 106048151
- Publisher
- Springer Japan
- Year
- 2002
- Tongue
- English
- Weight
- 93 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0911-0119
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π SIMILAR VOLUMES
A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n=p 2 for an odd prime p. We construct a family of ( p -1)/2 non-isomorphic perfect 1-factorisations of K n, n . Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin s
Given a set of valences ( ui) such that { ui> and (vi-k} are both realizable as valences of graphs without loops or multiple edges, an explicit conslruction method is described for obtaining a graph with valences {ui] having a k-factor. A number of extensions of the result are obtained. Similar resu
We prove the conjecture of Abbott and Katchalski that for every m ~> 2 there is a positive constant 2,. such that S(K~n ) >~ 2mnd-lS(Ka~ -1) where S(Ka~) is the length of the longest snake (cycle without chords) in the cartesian product K~ of d copies of the complete graph Kin. As a corollary, we co
## Abstract Let __Z__~__p__~ denote the cyclic group of order __p__ where __p__ is a prime number. Let __X__ = __X__(__Z__~__p__~, __H__) denote the Cayley digraph of __Z__~__p__~ with respect to the symbol __H__. We obtain a necessary and sufficient condition on __H__ so that the complete graph on