The aim of this paper is to characterize for every k ≥ 1 all (l + 3)-connected graphs G on n ≥ 3 vertices satisfying P(n + k): for each pair of vertices x and y in G, such that there is a path system S of length k with l internal vertices which components are paths of length at most 2 satisfying: such that S is not contained in any hamiltonian cycle of G.
patterns in pdf
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