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Minimum Degree, Leaf Number, and Hamiltonicity

S. Mukwembi
The American Mathematical Monthly
Vol. 120, No. 2 (February 2013), p. 115
DOI: 10.4169/amer.math.monthly.120.02.115
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Page Count: 1
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Abstract Let G be a finite connected graph with minimum degree δ > 4. The leaf number L(G) of G is defined as the maximum number of leaf vertices contained in a spanning tree of G. We show that if δ ≥ L(G) − 1, then G is Hamiltonian. This confirms, and improves, a conjecture of the computer program Graffiti.pc.

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