The $n$-adjacency graph for knots

Marion Campisi; Brandy Doleshal; Eric Staron

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arXiv · 2603.08597

The $n$-adjacency graph for knots

Marion Campisi·Brandy Doleshal·Eric Staron

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Abstract

A knot $K$ is called $n$-adjacent to a knot $K'$ if there is a set of $n$ crossing circles $\mathcal C$ in $K$ so that a generalized crossing change at any nonempty subset of crossings in $\mathcal C$ yields $K'$. In this paper, the authors define a new graph $\Gamma_n$ to represent $n$-adjacency relationships between knots. We prove several results about this new object.

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Marion Campisi, Brandy Doleshal, Eric Staron. 2026-03-09. The $n$-adjacency graph for knots. https://arxiv.org/abs/2603.08597

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