Large matchings from eigenvalues

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Bounds on graph eigenvalues II (2006, background): “Proof of inequality (2) when G is subregular As mentioned in the introduction, inequality (2) was first proved by Cioabă and Gregory [3].”
Principal eigenvectors of irregular graphs (2007, unknown): “6 and results from [3], we can show that if G is an irregular graph, then xmin ≤ ∆ − λ1 ∆ − 2e n · 1 √ n < ( 1 − 1 (∆ + 2)(n∆ − 2e) ) 1 √ n .”
A survey on spectral conditions for some extremal graph problems (2021, background): “[48] Let G be a connected k-regular graph on n vertices with eigenvalues k = λ1 ≥ λ2 ≥ λ3 ≥ · · · ≥ λn.”
Bounds on graph eigenvalues I (2006, background): “known facts about µ(G) is the inequality µ(G) ≥ 2m/n, due to Collatz and Sinogovitz [4]. In [11] we gave upper and lower bounds on µ(G)−2m/n in terms of degree deviation. In turn, Cioab˘a and Gregory [3] showed that, if G is irregular and n ≥ 4, then µ−2m/n > 1/(n∆ +2n). In this note we give anot”