Abstract
It is an interesting problem that how much connectivity ensures the existence ofn disjoint paths joining givenn pairs of vertices, but to get a sharp bound seems to be very difficult. In this paper, we study how muchgeodetic connectivity ensures the existence ofn disjointgeodesics joining givenn pairs of vertices, where a graph is calledk-geodetically connected if the removal of anyk−1 vertices does not change the distance between any remaining vertices.
Similar content being viewed by others
References
M. Behzad, G. Chartland andL. Lesniak-Foster,Graphs and Digraphs, Prindle, Weber & Schmidt, Boston MA, 1979.
R. C. Entringer, D. E. Jackson andP. J. Slater, Geodetic connectivity of graphs.IEEE Trans on Circuits and Systems 24 (1977), 460–463.
H. A. Jung, Eine Verallgemeinerung desn-fachen Zusammenhangs für Graphen,Math. Ann. 187 (1970), 95–103.
D. G. Larman andP. Mani, On the existence of certain configurations within graphs and the 1-skeleton of polytopes,Proc. London Math. Soc. 20 (1970), 144–160.
C. Thomassen, 2-linked graphs,Europ. J. Combinatorics 1 (1980), 371–378.