Well-balanced orientation conjecture for maximum total arc-connectivity

Let GG be a graph, let G\vec{G} be an orientation of GG, and let tac(G)tac(\vec{G}) denote its total arc-connectivity. An orientation maximizes total arc-connectivity when it maximizes tac(G)tac(\vec{G}) among all orientations of GG. Well-balanced orientation conjecture. Every graph GG has an orientation G\vec{G} that maximizes tac(G)tac(\vec{G}) and is well-balanced. The source presents this as a stronger statement than the conjecture about 2-edge-connected graphs and does not give a resolution.

Sources & referencesView supporting material

Primary source

Florian Hörsch, “On orientations maximizing total arc-connectivity”, arXiv:2305.08688 (2023).

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