Gutin, Gregory and Yeo, Anders (2001) Solution of a conjecture of Volkmann on the number of vertices in longest paths and cycles of strong semicomplete multipartite digraphs. Graphs and Combinatorics, 17 (3).
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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 lh2cm1, 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.
This is a Submitted version This version's date is: 2001 This item is not peer reviewed
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