Fan-type theorem for path-connectivity

Abstract

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.

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References

  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 

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Saito, A. Fan-type theorem for path-connectivity. Combinatorica 16, 433–437 (1996). https://doi.org/10.1007/BF01261327

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Mathematics Subject Classification (1991)

  • 05C38