A (D, c)-coloring of the complete graph K" is a coloring of the edges with c colors such that all monochromatic connected subgraphs have at most D vertices. Resolvable block designs with c parallel classes and with block size D are natural examples of (D, c)-colorings. However, (D, c)-colorings are
On biclique partitions of the complete graph
β Scribed by Bryan L. Shader
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 930 KB
- Volume
- 117
- Category
- Article
- ISSN
- 0012-365X
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The problem was posed of determining the biclique partition number of the complement of a Hamiltonian path (Monson, Rees, and Pullman, Bull. Inst. Combinatorics and Appl. 14 (1995), 17-86). We define the complement of a path P , denoted P , as the complement of P in K m,n where P is a subgraph of K
## Abstract Graham and Pollak [3] proved that __n__ β1 is the minimum number of edgeβdisjoint complete bipartite subgraphs into which the edges of __K__~__n__~ can be decomposed. Using a linear algebraic technique, Tverberg [2] gives a different proof of that result. We apply his technique to show
In this paDer,
A graph G is m-partite if its points can be partitioned into m subsets Yl, . . . . Vm such that every line joins a point in Vi with a point in Vi, i + j. A complete m-partite graph contains every line joining Vi with V-. A complete graph Kp has every pair of its p points adjacent. The nth interchang
The complete even k-partite graph K n,.n\* ,..., "\* is the complete k-partite graph where all the n,'s are even numbers. Orientable and nonorientable quadrangular embeddings are constructed for all these graphs.