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Solution of a Conjecture of Volkmann on the Number of Vertices in Longest Paths and Cycles of Strong Semicomplete Multipartite Digraphs

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Abstract.

 A digraph obtained by replacing each edge of a complete multipartite graph by an arc or a pair of mutually opposite arcs with the same end vertices is called a semicomplete multipartite digraph. L. Volkmann conjectured that l≤2c−1, where l (c, respectively) is the number of vertices in a longest path (longest cycle) of a strong semicomplete multipartite digraph. The bound on l is sharp. We settle this conjecture in affirmative.

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Received: October 26, 1998¶Final version received: August 16, 1999

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Gutin, G., Yeo, A. Solution of a Conjecture of Volkmann on the Number of Vertices in Longest Paths and Cycles of Strong Semicomplete Multipartite Digraphs. Graphs Comb 17, 473–477 (2001). https://doi.org/10.1007/s003730170022

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  • DOI: https://doi.org/10.1007/s003730170022

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