Large connected 1-binding even-order graphs have perfect matchings unless they are the join K1 ∨ (K_{n-5} ∪ K3 ∪ K1) when the A_α-spectral radius meets or exceeds that of the exception.
Wu, Characterizing spanning trees via the size or the spectral radius of graphs, Aequationes Math
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Tight spectral radius conditions guarantee perfect k-matchings in t-connected graphs, including those with fractional perfect matchings.
k-connected even-order graphs with fractional perfect matchings and distance spectral radius bounded above by that of K_k ∨ (kK_1 ∪ K_3 ∪ K_{n-2k-3}) contain perfect matchings when n ≥ 8k+6, except for the extremal graph itself.
citing papers explorer
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Perfect matchings and $A_{\alpha}$-spectral radius in 1-binding graphs
Large connected 1-binding even-order graphs have perfect matchings unless they are the join K1 ∨ (K_{n-5} ∪ K3 ∪ K1) when the A_α-spectral radius meets or exceeds that of the exception.
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Spectral radius and perfect k-matchings in t-connected graphs
Tight spectral radius conditions guarantee perfect k-matchings in t-connected graphs, including those with fractional perfect matchings.
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Distance spectral radius and perfect matchings in graphs with given fractional property
k-connected even-order graphs with fractional perfect matchings and distance spectral radius bounded above by that of K_k ∨ (kK_1 ∪ K_3 ∪ K_{n-2k-3}) contain perfect matchings when n ≥ 8k+6, except for the extremal graph itself.