The spectral Moon–Moser thresholds for non-Hamiltonian balanced bipartite graphs and non-traceable nearly balanced bipartite graphs remain sharp in the linear range n ≥ 2k (resp. n ≥ 2k+1), with unique extremal graphs.
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Sharp spectral Moon--Moser-type theorems in the linear range via feasible graph parameters
The spectral Moon–Moser thresholds for non-Hamiltonian balanced bipartite graphs and non-traceable nearly balanced bipartite graphs remain sharp in the linear range n ≥ 2k (resp. n ≥ 2k+1), with unique extremal graphs.