## 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. © 2002 Wiley Periodicals, Inc. J Grap
Decomposition of some planar graphs into trees
✍ Scribed by Vojislav Petrović
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 121 KB
- Volume
- 150
- Category
- Article
- ISSN
- 0012-365X
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## Abstract We investigate tree decompositions (__T__,(__X__~t~)~tϵV(T)~) whose width is “close to optimal” and such that all the subtrees of __T__ induced by the vertices of the graph are “small.” We prove the existence of such decompositions for various interpretations of “close to optimal” and “
with ␦ G G V r2 q 10 h V log V , and h y 1 divides E , then there is a decomposition of the edges of G into copies of H. This result is asymptotically the best possible for all trees with at least three vertices.
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