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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 \Gamma 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. Running title: Solution of a conjecture of Volkmann... (Update)
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BibTeX entry: (Update)
@misc{ gutin-solution,
author = "Gregory Gutin and Anders Yeo",
title = "Solution of a conjecture of Volkmann on the number of vertices in longest
paths and cycles of strong semicomplete multipartite digraphs",
url = "citeseer.ist.psu.edu/293326.html" }
Citations (may not include all citations):537 Graph Theory with Applications (context) - Bondy, Murty - 1976
18 Cycles and paths in semicomplete multipartite digraphs (context) - Gutin - 1995
10 Cycles in multipartite tournaments: results and problems (context) - Volkmann
6 Generalizations of tournaments: a survey - Bang-Jensen, Gutin - 1998
4 generalizations and special topics (context) - Reid - 1996
4 Spanning multipartite tournaments of semicomplete multiparti.. (context) - Volkmann - 1998
3 Diconnected orientation and a conjecture of Las Vergnas (context) - Bondy - 1976
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