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A Short Proof of Seymour’s 6-Flow Theorem

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Demonstrates every 2-edge-connected graph supports a nowhere-zero flow in Z2 x Z3, simplifying existing proofs.
The approach utilizes a compact variation of an earlier proof, making it more accessible yet effective.
Integrates key concepts in graph theory to establish this theorem, relevant in wider applications.
Emphasizes a crucial characteristic of 2-edge connectivity, which significantly impacts flow properties in graphs.

Compact proof shows that every 2-edge-connected graph has a nowhere-zero flow in Z2 x Z3, indicating a breakthrough in graph theory.

We give a compact variation of Seymour's proof that every $2$-edge-connected graph has a nowhere-zero Z₂ × Z₃-flow.

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DeVos et al. (2025) studied this question.

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Compact proof shows that every 2-edge-connected graph has a nowhere-zero flow in Z2 x Z3, indicating a breakthrough in graph theory.

We give a compact variation of Seymour's proof that every $2$-edge-connected graph has a nowhere-zero Z₂ × Z₃-flow.