Packing the Steiner trees of a graph
β Scribed by L. Petingi; M. Talafha
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 127 KB
- Volume
- 54
- Category
- Article
- ISSN
- 0028-3045
No coin nor oath required. For personal study only.
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## Abstract We prove that if __T__ is a tree of order __p__ β©Ύ 5 and __G__ is a graph of order __p__ and size __p__ β 1 such that neither __T__ nor __G__ is a star, then __T__ can be embedded in G, the complement of __G__.
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) wnΓ2x , then there are w |E |Γ(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
The average distance p(G) of a graph G is the average among the distances between all pairs of vertices in G. For n 2 2, the average Steiner n-distance ,4G) of a connected graph G is the average Steiner distance over all sets of n vertices in G. It is shown that for a connected weighted graph G, pu,