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arXiv · 2108.09363

A Pivot Gray Code Listing for the Spanning Trees of the Fan Graph

Ben Cameron·Aaron Grubb·Joe Sawada
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Abstract

We use a greedy strategy to list the spanning trees of the fan graph, $F_n$, such that successive trees differ by pivoting a single edge around a vertex. It is the first greedy algorithm for exhaustively generating spanning trees using such a minimal change operation. The resulting listing is then studied to find a recursive algorithm that produces the same listing in $O(1)$-amortized time using $O(n)$ space. Additionally, we present $O(n)$-time algorithms for ranking and unranking the spanning trees for our listing; an improvement over the generic $O(n^3)$-time algorithm for ranking and unranking spanning trees of an arbitrary graph.

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Ben Cameron, Aaron Grubb, Joe Sawada. 2021-08-20. A Pivot Gray Code Listing for the Spanning Trees of the Fan Graph. https://arxiv.org/abs/2108.09363

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