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Minimum orders of eulerian oriented digraphs with given diameter

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Abstract

A digraph D is oriented if it does not contain 2-cycles. If an oriented digraph D has a directed eulerian path, it is an oriented eulerian digraph. In this paper, when an oriented eulerian digraph D has minimum out-degree 2 and a diameter d, we find the minimum order of D. In addition, when D is 2-regular with diameter 4m (m ≥ 2), we classify the extremal cases.

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Authors and Affiliations

  1. Department of Mathematics, University of Incheon, Incheon, 402-749, Korea

    Yoomi Rho

  2. Department of Mathematics, Gangneung-Wonju National University, Gangneung, 210-702, Korea

    Byeong Moon Kim & Byung Chul Song

  3. Department of Information and Mathematics, Korea University, Sejong, 339-700, Korea

    Woonjae Hwang

Authors
  1. Yoomi Rho
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  2. Byeong Moon Kim
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  3. Woonjae Hwang
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  4. Byung Chul Song
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Corresponding author

Correspondence to Byung Chul Song.

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Supported by the University of Incheon Research Grant in 2009-2010

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Rho, Y., Kim, B.M., Hwang, W. et al. Minimum orders of eulerian oriented digraphs with given diameter. Acta. Math. Sin.-English Ser. 30, 1125–1132 (2014). https://doi.org/10.1007/s10114-014-3194-4

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  • DOI: https://doi.org/10.1007/s10114-014-3194-4

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