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connected graph; geodetic graph; bipartite graph; route system; shortest paths
The concept of a route system was introduced by the present author in [3].Route systems of a connected graph $G$ generalize the set of all shortest paths in $G$. In this paper some properties of route systems are studied.
[1] M. Behzad G. Chartrand, and L. Lesniak-Foster: Graphs & Digraphs. Prindle, Weber & Schmidt, Boston, 1979. MR 0525578
[2] L. Nebeský: On certain extensions of intervals in graphs. Čas. pěst. mat. 115 (1990), 171-177. MR 1054004
[3] L. Nebeský: Route systems and bipartite graphs. Czechoslovak Math. Journal 41 (116) (1991), 260-264. MR 1105440
[4] L. Nebeský: A characterization of the set of all shortest paths in a connected graph. Mathematica Bohemica 119 (1994), 15-20. MR 1303548
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