On the tree packing conjecture

Authors

Cory T. Palmer, University of Illinois at Urbana-Champaign, C & O Candidate

Document Type

Presentation Abstract

Presentation Date

3-14-2013

Abstract

A set of graphs is said to pack into the complete graph, K_n, if the graphs can be found as edge-disjoint subgraphs of K_n. In 1978, Gyarfas conjectured that any set of n-1 trees T₁, T₂, ..., T_n-1 such that T_i has n-i edges packs into K_n. Even when we weaken the statement to claim that the largest t trees T₁, T₂, ..., T_t pack into K_n the conjecture remains open. Among others we will discuss our recent result that any t=(1/10)n^¼ trees T₁, T₂, ..., T_t such that T_i has n-i edges packs into K_n+1 (for n large enough). (This is joint work with J. Balogh.)

Additional Details

Thursday, 14 March 2013
3:10 p.m. in Math 103
4:00 p.m. Refreshments in Math Lounge 109

Recommended Citation

Palmer, Cory T., "On the tree packing conjecture" (2013). Colloquia of the Department of Mathematical Sciences. 421.
https://scholarworks.umt.edu/mathcolloquia/421