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

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Computing and Combinatorics (COCOON 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 13025))

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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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Authors and Affiliations

  1. University of Guelph, Guelph, Canada

    Ben Cameron, Aaron Grubb & Joe Sawada

Authors
  1. Ben Cameron
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  2. Aaron Grubb
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  3. Joe Sawada
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Corresponding author

Correspondence to Aaron Grubb .

Editor information

Editors and Affiliations

  1. National Cheng Kung University, Tainan, Taiwan

    Chi-Yeh Chen

  2. National Tsing Hua University, Hsinchu, Taiwan

    Wing-Kai Hon

  3. National Taipei University of Business, Taoyuan, Taiwan

    Ling-Ju Hung

  4. National Taitung University, Taitung, Taiwan

    Chia-Wei Lee

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Cameron, B., Grubb, A., Sawada, J. (2021). A Pivot Gray Code Listing for the Spanning Trees of the Fan Graph. In: Chen, CY., Hon, WK., Hung, LJ., Lee, CW. (eds) Computing and Combinatorics. COCOON 2021. Lecture Notes in Computer Science(), vol 13025. Springer, Cham. https://doi.org/10.1007/978-3-030-89543-3_5

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  • DOI: https://doi.org/10.1007/978-3-030-89543-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-89542-6

  • Online ISBN: 978-3-030-89543-3

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