Holub–Lužar–Mihaliková–Mockovčiaková–Soták's large cycle product conjecture

From papers

Let CmC_m and CnC_n be cycles, and let CmCnC_m\square C_n denote their Cartesian product.

Holub–Lužar–Mihaliková–Mockovčiaková–Soták's stronger conjecture. There exists a constant cc such that for all integers m,ncm,n\geq c,

χst(CmCn)=6.\chi'_{st}(C_m\square C_n)=6.

This is presented in the survey as a stronger, lower-confidence version of the preceding cycle product conjecture. The known general bound is 6χst(CmCn)76\leq\chi'_{st}(C_m\square C_n)\leq7, and the asserted uniform eventual equality remains open.

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Sources & referencesView supporting material

Primary source

Hui Lei and Yongtang Shi, “A survey on star edge-coloring of graphs”, arXiv:2009.08017 (2020).

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