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
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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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DOI: https://doi.org/10.1007/BF01261327