In this note we improve significantly the result appeared in [4] by showing that any sequence of trees { T2, 'I;, . , T,} can be packed into the complete bipartite graph K,\_,,n,z (n even) for f = 0.3n. Furthermore we support Fishburn's Conjecture [2] by showing that any sequence {T,, T4,
On packing trees into complete bipartite graphs
β Scribed by Raphael Yuster
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 124 KB
- Volume
- 163
- Category
- Article
- ISSN
- 0012-365X
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For two integers a and b, we say that a bipartite graph G admits an (a, b)bipartition if G has a bipartition (X, Y ) such that |X| = a and |Y | = b. We say that two bipartite graphs G and H are compatible if, for some integers a and b, both G and H admit (a, b)-bipartitions. In this paper, we prove
## Abstract In this study, we provide methods for drawing a tree with __n__ vertices on a convex polygon, without crossings and using the minimum number of edges of the polygon. We apply the results to obtain planar packings of two trees in some specific cases. Β© 2002 Wiley Periodicals, Inc. J Grap
For two integers a and b, we say that a bipartite graph G admits an ( a , b)-bipartition if G has a bipartition ( X , Y ) such that /XI = a and ( Y / = b. We say that two bipartite graphs G and H are compatible if, for some integers a and b, both G and H admit ( a , b)-bipartitions. In this note, w
## Abstract A short proof is given of the impossibility of decomposing the complete graph on __n__ vertices into __n__β2 or fewer complete bipartite graphs.