On $t$-intersecting Families of Spanning Trees
Pitchayut Saengrungkongka

TL;DR
This paper establishes an optimal upper bound on the size of collections of spanning trees in a complete graph where every pair shares at least t edges, extending previous results to larger t values.
Contribution
It proves a tight bound for the maximum size of t-intersecting spanning tree families in complete graphs, improving earlier bounds for larger t.
Findings
Bound is tight and achieved by fixing t disjoint edges.
Extends previous results to larger t values.
Provides a new combinatorial bound for intersecting spanning trees.
Abstract
We prove that there exists a constant such that for all integers , if is a collection of spanning trees in such that any two intersect at at least edges, then . This bound is tight; the equality is achieved when is a collection of spanning trees containing a fixed disjoint edges. This is an improvement of a result by Frankl, Hurlbert, Ihringer, Kupavskii, Lindzey, Meagher, and Pantagi, who proved such a result for .
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Taxonomy
TopicsAdvanced Graph Theory Research · Optimization and Search Problems · Complexity and Algorithms in Graphs
