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Mathematical Sciences
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"Turán numbers for forests"
Cory Palmer
University of Montana
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)
Monday, 3 February 2014
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109
Spring 2014 Colloquia & Events
Mathematical Sciences | University of Montana