Li-Li Undirected Multiple-Unicast Network Coding Conjecture

For every finite undirected edge-capacitated network and every finite collection of independent source-destination unicast sessions, prove or disprove that the zero-error network-coding capacity region equals the fractional multicommodity-routing capacity region. Each undirected edge has a shared capacity bounding the sum of transmission rates in its two directions; intermediate nodes may causally encode received messages in the coding model. Fractional routing may split each session over paths. The target uses the standard zero-error formulation, not multicast or directed networks.

Source: Sirui Liu, Li Que, Zongpeng Li and Baochun Li, On the Multiple-Unicast Conjecture: Beyond Cut Metrics, arXiv:2608.06070v1 (2026).

Status Open · subcases solved Status review date not recorded in this edition

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