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arXiv · 1903.02508

Longest paths in 2-edge-connected cubic graphs

Nikola K. Blanchard·Eldar Fischer·Oded Lachish·Felix Reidl
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Abstract

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 $\Omega\left(\frac{\log^2{n}}{\log{\log{n}}}\right)$, and (ii) there exists a $2$-edge-connected cubic graph, such that every path in the graph has length $O(\log^2{n})$.

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Nikola K. Blanchard, Eldar Fischer, Oded Lachish, Felix Reidl. 2019-03-06. Longest paths in 2-edge-connected cubic graphs. https://arxiv.org/abs/1903.02508

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