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Bipartite partial duals and circuits in medial graphs

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Abstract

It is well known that a plane graph is Eulerian if and only if its geometric dual is bipartite. We extend this result to partial duals of plane graphs. We then characterize all bipartite partial duals of a plane graph in terms of oriented circuits in its medial graph.

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Authors and Affiliations

  1. School of Computing and Mathematics, University of Plymouth, PL4 8AA, Devon, UK

    Stephen Huggett

  2. Department of Mathematics Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    Iain Moffatt

Authors
  1. Stephen Huggett
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  2. Iain Moffatt
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Correspondence to Stephen Huggett.

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Huggett, S., Moffatt, I. Bipartite partial duals and circuits in medial graphs. Combinatorica 33, 231–252 (2013). https://doi.org/10.1007/s00493-013-2850-0

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  • DOI: https://doi.org/10.1007/s00493-013-2850-0

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