Document Type
Lecture
Publication Date
3-5-2025
Abstract
A family of spanning trees of the complete graph on n vertices Kn is t-intersecting if any two members have a forest on t edges in common. We prove an ErdosKo Rado result for t-intersecting families of spanning trees of Kn. In particular, we show there exists a constant C > 0 such that for all n C(logn)t, the largest t-intersecting families of spanning trees of Kn are the families consisting of all spanning trees that contain a xed set of t disjoint edges (as well as the stars on n vertices for t = 1). The proof uses the spread approximation technique in conjunction with the Lopsided Lovasz Local Lemma. This is joint work with Peter Frankl, Glenn Hurlbert, Ferdinand Ihringer, Andrey Kupavskii, Karen Meagher, and Venkata Raghu Tej Pantangi.
Relational Format
presentation
Recommended Citation
Lindzey, Nathan, "Intersecting Families of Spanning Trees" (2025). Combinatorics Seminar. 1.
https://egrove.olemiss.edu/math_combinatorics/1
