Year: 2025
Type: preprint
Abstract: We prove that the set of the smallest eigenvalues attained by $3$-colorable graphs is dense in $(-\infty, -λ^*)$, where $λ^* = ρ^{1/2} + ρ^{-1/2} \approx 2.01980$ and $ρ$ is the positive real root of $x^3 = x + 1$. As a consequence, in the context of spherical two-distance sets, our result precludes any further refinement of the forbidden-subgraph method through the chromatic number of signed graphs.
Source: arXiv (Cornell University)
Authors: Jiang, Zilin, Wang, Zhiyu
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415246722
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