Tight spectral radius conditions guarantee perfect k-matchings in t-connected graphs, including those with fractional perfect matchings.
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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.
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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.