Abstract

Let G be a simple connected graph with minimum degree δ. Then G is Hamiltonian if it contains a spanning cycle and traceable if it contains a spanning path. The leaf number L(G) of G is defined as the maximum number of end vertices contained in a spanning tree of G. We prove a sufficient condition, depending on L(G) and δ, for G to be Hamiltonian or traceable. Our results, apart from providing a new sufficient condition for Hamiltonicity, settle completely a conjecture of the computer program, Graffiti.pc, instructed by DeLaViña.

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