Abstract.
In 1975, Lovász conjectured that for any positive integer k, there exists a minimum positive integer f(k) such that, for any two vertices x, y in any f(k)-connected graph G, there is a path P from x to y in G such that G−V(P) is k-connected. A result of Tutte implies f(1) = 3. Recently, f(2) = 5 was shown by Chen et al. and, independently, by Kriesell. In this paper, we show that f(2) = 4 except for double wheels.
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Received October 17, 2003
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Kawarabayashi, Ki., Lee, O. & Yu, X. Non-Separating Paths in 4-Connected Graphs. Ann. Comb. 9, 47–56 (2005). https://doi.org/10.1007/s00026-005-0240-4
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DOI: https://doi.org/10.1007/s00026-005-0240-4