Let H be a tree on h 2 vertices. It is shown that if n is sufficiently large and G=(V, E ) is an n-vertex graph with $(G) wnÂ2x , then there are w |E |Â(h&1)x edge-disjoint subgraphs of G which are isomorphic to H. In particular, if h&1 divides |E | then there is an H-decomposition of G. This result
Packing trees into planar graphs
✍ Scribed by A. García; C. Hernando; F. Hurtado; M. Noy; J. Tejel
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 108 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
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 Graph Theory 40: 172–181, 2002
📜 SIMILAR VOLUMES
## Abstract It is proven that each maximal planar bipartite graph is decomposable into two trees. © 1993 John Wiley & Sons, Inc.
We prove the conjecture made by \(\mathrm{O}\). V. Borodin in 1976 that the vertex set of any planar graph can be decomposed into two sets such that one of them induces a 3-degenerate graph and the other induces a 2-degenerate graph. that is, a forest. c. 1995 Academic Press. Inc.