Fan-type theorem for path-connectivity


A graphG is said to bek-path-connected if every pair of distinct vertices inG are joined by a path of length at leastk. We prove that if max{deg G x, deg G y}≥k for every pair of verticesx,y withd G (x,y)=2 in a 2-connected graphG, whered G (x,y) is the distance betweenx andy inG, thenG isk-path-connected.

This is a preview of subscription content, access via your institution.


  1. [1]

    G. Chartrand, andL. Lesniak:Graphs & Digraphs, (2nd ed.), Wadsworth & Brooks/Cole, Monterey, CA (1986).

    Google Scholar 

  2. [2]

    G. H. Fan: New sufficient conditions for cycles in graphs,J. Combin. Theory Ser. B,37 (1984), 221–227.

    Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Saito, A. Fan-type theorem for path-connectivity. Combinatorica 16, 433–437 (1996).

Download citation

Mathematics Subject Classification (1991)

  • 05C38