SEARCH

SEARCH BY CITATION

Keywords:

  • graph design;
  • graph decomposition;
  • complete bipartite graph

Abstract

A decomposition of a complete graph inline image into disjoint copies of a complete bipartite graph inline image is called a inline image-design of order n. The existence problem of inline image-designs has been completely solved for the graphs inline image for inline image, inline image for inline image, K2, 3 and K3, 3. In this paper, I prove that for all inline image, if there exists a inline image-design of order N, then there exists a inline image-design of order n for all inline image (mod inline image) and inline image. 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.