article published yes Xiaoyu He author Yuval Wigderson author 2d0023a0-1567-11f0-833d-d5c1e476d4b5 Extending a recent breakthrough of Shitov, we prove that the chromatic number of the tensor product of two graphs can be a constant factor smaller than the minimum chromatic number of the two graphs. More precisely, we prove that there exists an absolute constant δ>0 such that for all c sufficiently large, there exist graphs G and H with chromatic number at least (1+δ)c for which χ(G×H)≤c. Elsevier2021 eng Graph coloringHedetniemi's conjecture 0095-8956 1906.0678310.1016/j.jctb.2020.03.003 146485-494 yes X. He, Y. Wigderson, Journal of Combinatorial Theory, Series B 146 (2021) 485–494. He, Xiaoyu, and Yuval Wigderson. “Hedetniemi’s Conjecture Is Asymptotically False.” <i>Journal of Combinatorial Theory, Series B</i>. Elsevier, 2021. <a href="https://doi.org/10.1016/j.jctb.2020.03.003">https://doi.org/10.1016/j.jctb.2020.03.003</a>. X. He and Y. Wigderson, “Hedetniemi’s conjecture is asymptotically false,” <i>Journal of Combinatorial Theory, Series B</i>, vol. 146. Elsevier, pp. 485–494, 2021. He, Xiaoyu, and Yuval Wigderson. “Hedetniemi’s Conjecture Is Asymptotically False.” <i>Journal of Combinatorial Theory, Series B</i>, vol. 146, Elsevier, 2021, pp. 485–94, doi:<a href="https://doi.org/10.1016/j.jctb.2020.03.003">10.1016/j.jctb.2020.03.003</a>. He X, Wigderson Y. Hedetniemi’s conjecture is asymptotically false. <i>Journal of Combinatorial Theory, Series B</i>. 2021;146:485-494. doi:<a href="https://doi.org/10.1016/j.jctb.2020.03.003">10.1016/j.jctb.2020.03.003</a> He, X., &#38; Wigderson, Y. (2021). Hedetniemi’s conjecture is asymptotically false. <i>Journal of Combinatorial Theory, Series B</i>. Elsevier. <a href="https://doi.org/10.1016/j.jctb.2020.03.003">https://doi.org/10.1016/j.jctb.2020.03.003</a> He X, Wigderson Y. 2021. Hedetniemi’s conjecture is asymptotically false. Journal of Combinatorial Theory, Series B. 146, 485–494. 221562026-06-29T10:50:09Z2026-07-08T07:43:57Z