3 research outputs found
Embedding a Forest in a Graph
For \math{p\ge 1}, we prove that every forest with \math{p} trees whose sizes
are can be embedded in any graph containing at least
vertices and having a minimum degree at least
.Comment: Working paper, submitte
On the Turan number of forests
The Turan number of a graph H, ex(n,H), is the maximum number of edges in a
graph on n vertices which does not have H as a subgraph. We determine the Turan
number and find the unique extremal graph for forests consisting of paths when
n is sufficiently large. This generalizes a result of Bushaw and Kettle [
Combinatorics, Probability and Computing 20:837--853, 2011]. We also determine
the Turan number and extremal graphs for forests consisting of stars of
arbitrary order