Abstract
A simple graph G on n vertices satisfies property Pi if between every pair of distinct vertices of G, there exists a path with i vertices. In this paper known results and open questions about the relationship between property Pi and property Pj are considered. There are degree conditions, edge conditions and the condition of being the power of a graph which guarantee that a graph is Hamiltonian-connected (satisfies property Pn). Included is a discussion of these conditions and their relationship to property Pi for i ≠ n.
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© 1978 Springer-Verlag Berlin Heidelberg
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Faudree, R.J., Schelp, R.H. (1978). Various length paths in graphs. In: Alavi, Y., Lick, D.R. (eds) Theory and Applications of Graphs. Lecture Notes in Mathematics, vol 642. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0070373
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DOI: https://doi.org/10.1007/BFb0070373
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