The half-flow-pair conjecture

A tt-flow-pair is the flow-pair notion defined in the paper, consisting of a 22-flow and a second integer flow satisfying the prescribed nonzero-value and magnitude conditions for parameter tt.

Half-flow-pair conjecture. Every bridgeless graph admits a 1/21/2-flow-pair.

The source states that this conjecture is stronger than both Tutte's 55-flow conjecture and the two-dimensional Chebyshev bound Φ2(G)5/2\Phi^\infty_2(G)\leq 5/2. It is presented as open.

Sources & referencesView supporting material

Primary source

Lukáš Gáborik, Sascha Kurz, Giuseppe Mazzuoccolo, Jozef Rajník and Florian Rieg, “Manhattan and Chebyshev flows”, arXiv:2510.22234 (2025).

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