Strengthened Chvátal–Erdős, McDiarmid–Yolov, connected-dominating-set, and bipartite Hamiltonicity conditions all force the Hamilton cycles to span the entire cycle space.
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On graphs whose cycle space is spanned by their Hamilton cycles
Strengthened Chvátal–Erdős, McDiarmid–Yolov, connected-dominating-set, and bipartite Hamiltonicity conditions all force the Hamilton cycles to span the entire cycle space.