Minimum Orders of Eulerian Oriented Digraphs with Given Diameter

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Minimum Orders of Eulerian Oriented Digraphs with Given Diameter

Rho, Yoomi; Kim, Byeong Moon; Hwang, Woonjae; Song, Byung Chul

Acta mathematica Sinica. English series, 07/2014, Volume: 30, Issue: 7

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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 4rn （m≥2）, we classify the extremal cases.

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Rho, Yoomi | Kim, Byeong Moon | Hwang, Woonjae | Song, Byung Chul

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