A complete t-intersection theorem for families of spanning trees

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This is a Quantitative Study study.

Elizaveta Iarovikova; Andrey Kupavskii

doi:10.48550/arxiv.2507.17913

July 23, 2025Open Access

A complete t-intersection theorem for families of spanning trees

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Key Points

The study establishes the size of the largest t-intersecting family for spanning trees in complete graphs.
It shows that for n greater than n_0, families exist with significant t-intersections, revealing structural properties.
Analysis is conducted on the general condition of t values up to n-1, indicating a complete theorem solution.
The findings highlight a unique instance where a full t-intersection theorem for this structure is achieved.

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Implication

This analysis determines the largest t-intersecting family of spanning trees in K_n, suggesting new insights into combinatorial structures.

Abstract

Let Tₙ denote the set of all labelled spanning trees of Kₙ. A family F ⊂ Tₙ is t-intersecting if for all A, B ∈ F the trees A and B share at least t edges. In this paper, we determine for n>n₀ the size of the largest t-intersecting family F⊂ Tₙ for all meaningful values of t (t≤ n-1). This result is a rare instance when a complete t-intersection theorem for a given type of structures is known.

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Cite This Study

Iarovikova et al. (2025) studied this question.

synapsesocial.com/papers/68f19f20de32064e504ddde1 https://doi.org/10.48550/arxiv.2507.17913

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A complete t-intersection theorem for families of spanning trees

Key Points

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Implication

Abstract

Discussion

Cite This Study

A complete t-intersection theorem for families of spanning trees

Key Points

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Implication

Abstract

Discussion

Cite This Study

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