Longest paths in 2-edge-connected cubic graphs

03/06/2019

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by   Nikola K. Blanchard, et al.

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We prove almost tight bounds on the length of paths in 2-edge-connected cubic graphs. Concretely, we show that (i) every 2-edge-connected cubic graph of size n has a path of length Ω(^2n/n), and (ii) there exists a 2-edge-connected cubic graph, such that every path in the graph has length O(^2n).