Turán numbers for forests

Authors

Cory Palmer, University of Montana

Document Type

Presentation Abstract

Presentation Date

2-3-2014

Abstract

The Turán number of a graph H, ex(n,H), is the maximum number of edges in a graph on n vertices which does not contain H as a subgraph. The Erdős-Stone-Simonovits Theorem establishes (essentially) ex(n,H) for graphs H of chromatic number 3 or greater. For bipartite graphs much is still unknown. Of particular interest is the Turán number for trees (this is the Erdős-Sós conjecture). We will concentrate our attention on the Turán number of forests. Bushaw and Kettle determined the Turán number of a forest made up of copies of a path of a fixed length. We generalize their result by finding the Turán number for a forest made of up arbitrary length paths. We also determine the Turán number for a forest made up of arbitrary size stars. In both cases we characterize the extremal graphs.

(joint work with Hong Liu and Bernard Lidický)

Additional Details

Monday, February 3 at 3:10 p.m. in Math 103

Recommended Citation

Palmer, Cory, "Turán numbers for forests" (2014). Colloquia of the Department of Mathematical Sciences. 443.
https://scholarworks.umt.edu/mathcolloquia/443