The conjecture that every 3-edge-connected graph has Frank number at most 3

From papers

Let GG be a 33-edge-connected graph. Its Frank number f(G)f(G) is the minimum number of orientations needed so that every edge is deletable in at least one of them. Frank-number conjecture. Every 33-edge-connected graph GG satisfies

f(G)3.f(G)\leq 3.

The paper proves the general upper bound f(G)7f(G)\leq 7, obtains f(G)=3f(G)=3 for the Petersen graph, and gives improved bounds for more restricted graph classes. Improving the general bound to 33 remains open.

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Sources & referencesView supporting material

Primary source

Florian Hörsch and Zoltán Szigeti, “Connectivity of orientations of 3-edge-connected graphs”, arXiv:2012.03259 (2020).

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