Subtrees and Subforests of Graphs
β Scribed by S. Brandt
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 299 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
β¦ Synopsis
In this paper we present sufficient edge-number and degree conditions for a graph to contain all forests of given size. The edge-number bound answers in the aflirmative a conjecture due to ErdΕs and SΓ³s. Furthermore, we will give improved bounds for specified spanning subtrees of graphs. 1994 Academic Press, Inc.
π SIMILAR VOLUMES
Our paper proves special eases of the following conjecture: for any fined tr~,e "J~ there exists a natural number f = fiT) ~o that every triangle-free graph of chromatic number ] T) contains T as au induced subgraph. The main ;csult concerns the case when T has radius two.
## Abstract A necessary condition for the decomposition of a tree __T__ into subtrees, each isomorphic to a tree from a given set of trees is presented. We also present a characterization of the set of trees for which the condition is sufficient. Many examples are given.
## Abstract A hypergraph __H__ = (__V__,__E__) is a subtree hypergraph if there is a tree __T__ on __V__ such that each hyperedge of __E__ induces a subtree of __T__. Since the number of edges of a subtree hypergraph can be exponential in __n__ = |__V__|, one can not always expect to be able to fin