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The Interchange Graphs of Tournaments with Minimum Score Vectors Are Exactly Hypercubes

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Abstract

A Δ-interchange is a transformation which reverses the orientations of the arcs in a 3-cycle of a digraph. Let \({\fancyscript T}(S)\) be the collection of tournaments that realize a given score vector S. An interchange graph of S, denoted by G(S), is an undirected graph whose vertices are the tournaments in \({\fancyscript T}(S)\) and an edge joining tournaments \(T,T' \in {\fancyscript T}(S)\) provided T′ can be obtained from T by a Δ-interchange. In this paper, we find a set of score vectors of tournaments for which the corresponding interchange graphs are hypercubes.

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Authors and Affiliations

  1. Department of Information Management, National Taipei College of Business, Taipei, Taiwan, ROC

    An–Hang Chen & Jou–Ming Chang

  2. Department of Information Management, National Taiwan University of Science and Technology, Taipei, Taiwan, ROC

    Yue–Li Wang

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  1. An–Hang Chen
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  2. Jou–Ming Chang
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  3. Yue–Li Wang
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Correspondence to Yue–Li Wang.

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Chen, A., Chang, J. & Wang, Y. The Interchange Graphs of Tournaments with Minimum Score Vectors Are Exactly Hypercubes. Graphs and Combinatorics 25, 27–34 (2009). https://doi.org/10.1007/s00373-008-0818-4

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  • DOI: https://doi.org/10.1007/s00373-008-0818-4

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