Decomposition of Complete Graphs into Isomorphic Complete Bipartite Graphs
Version of Record online: 16 NOV 2012
© 2012 Wiley Periodicals, Inc.
Journal of Combinatorial Designs
Volume 21, Issue 11, pages 524–530, November 2013
How to Cite
Kolotoğlu, E. (2013), Decomposition of Complete Graphs into Isomorphic Complete Bipartite Graphs. J. Combin. Designs, 21: 524–530. doi: 10.1002/jcd.21335
- Issue online: 3 SEP 2013
- Version of Record online: 16 NOV 2012
- Manuscript Revised: 11 SEP 2012
- Manuscript Received: 8 MAY 2012
- graph design;
- graph decomposition;
- complete bipartite graph
A decomposition of a complete graph into disjoint copies of a complete bipartite graph is called a -design of order n. The existence problem of -designs has been completely solved for the graphs for , for , K2, 3 and K3, 3. In this paper, I prove that for all , if there exists a -design of order N, then there exists a -design of order n for all (mod ) and . Giving necessary direct constructions, I provide an almost complete solution for the existence problem for complete bipartite graphs with fewer than 18 edges, leaving five orders in total unsolved.