Cho–Hyun–O–Park spectral-radius conjecture for [a,b]-factors

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Let aa and bb be positive integers with a≤ba\le b, and let GG be a finite undirected simple connected graph of order nn satisfying

n≥a+1,na≡0(mod2).n\ge a+1,\qquad na\equiv 0\pmod{2}.

For a graph HH, write ρ(H)\rho(H) for its spectral radius, and call a spanning subgraph an [a,b][a,b]-factor if every vertex has degree between aa and bb in that subgraph. Cho–Hyun–O–Park conjecture. If

ρ(G)>ρ(Ka−1∨(Kn−a∪K1)),\rho(G)>\rho\bigl(K_{a-1}\vee(K_{n-a}\cup K_1)\bigr),

then GG contains an [a,b][a,b]-factor. This is a proposed spectral-radius sufficient condition for the existence of bounded-degree spanning factors; its resolution is not supplied in the source.

References

Primary source

Yuanyuan Chen, Huiqiu Lin and Shucheng Li, “Spectral radius, toughness and k-factor of graphs”, arXiv:2602.21577 (2026).

Additional references

4 papers in this index state this conjecture (2021–2026). The statement above is taken from the most recent of them; the others are arXiv:2509.00769, arXiv:2312.15902, arXiv:2111.01367.

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