Contract grant sponsor: Department of Science and Technology, Goverment of India; Contract grant number: DST/INSPIRE Fellowship/2011-IF110084.
Cycle Frames of Complete Multipartite Multigraphs - III
Article first published online: 16 SEP 2013
© 2013 Wiley Periodicals, Inc.
Journal of Combinatorial Designs
Volume 22, Issue 11, pages 473–487, November 2014
How to Cite
Muthusamy, A. and Vadivu, A. S. (2014), Cycle Frames of Complete Multipartite Multigraphs - III. J. Combin. Designs, 22: 473–487. doi: 10.1002/jcd.21373
- Issue published online: 8 SEP 2014
- Article first published online: 16 SEP 2013
- Manuscript Revised: 23 AUG 2013
- Manuscript Received: 8 APR 2013
- Department of Science and Technology, Government of India. Grant Number: DST/INSPIRE Fellowship/2011-IF110084
- cycle frame
For two graphs G and H their wreath product has vertex set in which two vertices and are adjacent whenever or and . Clearly, , where is an independent set on n vertices, is isomorphic to the complete m-partite graph in which each partite set has exactly n vertices. A 2-regular subgraph of the complete multipartite graph containing vertices of all but one partite set is called partial 2-factor. For an integer λ, denotes a graph G with uniform edge multiplicity λ. Let J be a set of integers. If can be partitioned into edge-disjoint partial 2-factors consisting cycles of lengths from J, then we say that has a -cycle frame. In this paper, we show that for and , there exists a -cycle frame of if and only if and . In fact our results completely solve the existence of a -cycle frame of .