Solution of a Conjecture of Volkmann on the Number of Vertices in Longest Paths and Cycles of Strong Semicomplete Multipartite Digraphs
- 29 Downloads
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.
KeywordsLonge Path Longe Cycle Complete Multipartite Graph Semicomplete Multipartite Digraph
Unable to display preview. Download preview PDF.