## Abstract It is known that a necessary condition for the existence of a 1βrotational 2βfactorization of the complete graph __K__~2__n__+1~ under the action of a group __G__ of order 2__n__ is that the involutions of __G__ are pairwise conjugate. Is this condition also sufficient? The complete ans
Some results on odd factors of graphs
β Scribed by Cui Yuting; Mikio Kano
- Publisher
- John Wiley and Sons
- Year
- 1988
- Tongue
- English
- Weight
- 245 KB
- Volume
- 12
- Category
- Article
- ISSN
- 0364-9024
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π SIMILAR VOLUMES
It was shown in a recent paper that an rs-regular multigraph G with maximum multiplicity Β΅(G) β€ r can be factored into r regular simple graphs if first we allow the deletion of a relatively small number of hamilton cycles from G. In this paper, we use this theorem to obtain extensions of some factor
Let I(t) be the set of integers with the property that in every Pt-free connected graph G, the i-center C,(G) induces a connected subgraph. What is the minimum element of /(t)? In this paper, we prove that this minimum is [2t/3] -1 if t = 0 or Z(mod3) and is [ 2 t / 3 ] otherwise. Furthermore, as co
## Abstract A (__g__, __f__)βfactor of a graph is a subset __F__ of __E__ such that for all $v \in V$, $g(v)\le {\rm deg}\_{F}(v)\le f(v)$. Lovasz gave a necessary and sufficient condition for the existence of a (__g__, __f__)βfactor. We extend, to the case of edgeβweighted graphs, a result of Kano
It is shown that, for a positive integer s, there exists an s-transitive graph of odd order if and only if s 3 and that, for s=2 or 3, an s-transitive graph of odd order is a normal cover of a graph for which there is an automorphism group that is almost simple and s-transitive.