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arXiv · 2610.07968

An independent computer-assisted proof of the Chen-Raspaud conjecture for k=4

Marysia Nazarczuk
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Abstract

We give an independent computer-assisted proof of the k=4 case of the Chen-Raspaud conjecture. We prove that every graph G with odd-girth(G) >= 9 and mad(G) < 9/4 admits a homomorphism to the Kneser graph K(9,4). The proof combines a minimal-counterexample argument with a rooted star replacement, exact finite computations in K(9,4), and a final charging argument. After all reducible local types are removed, the unique positive local type is (3,3,4). Its unit excess is transferred through its 4-thread to a relative with sufficient negative capacity. The computer-assisted statements used in the proof are certified by exact C++ bitset verifiers, and a separate Python implementation provides an independent cross-check; the complete source code and raw certificates accompany the manuscript.

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Marysia Nazarczuk. 2026-10-06. An independent computer-assisted proof of the Chen-Raspaud conjecture for k=4. https://arxiv.org/abs/2610.07968

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