TATERS

The classical Erdős-Ko-Rado theorem characterizes the maximum intersecting families of $k$-sets in $[n]$. Several analogs of these results arise from varying the ambient family and notion of intersection. Examples of such variations (in the ambient family) include characterizing the largest intersecting families of: permutations of a set, subspaces of a vector space, and triangulations of a convex $n$-gon.

In a recent paper, Frankl et al. characterize maximum $t$-intersecting families of spanning trees of $K_n$, for $n$ sufficiently large. They use a probabilistic tool in conjunction with an extramal set theoretic one, namely, the Lopsided Lovász Local Lemma (LLLL) and the recently developed spread approximation technique.

In this talk we present results on maximum $t$-intersecting families of $K_{n,n}$ where we replace the probabilistic tools (LLLL) of Frankl et al. with a spectral graph theoretic one - Laplacian eigenvalues of graphs.    

This is based on joint work with Gordian Bruns, Alexander Gavrilyuk, Josias Gomez and Nathan Lindzey.