Spanning paths in graphs

The Conjecture, Graffiti.pc 190, of the computer program Graffiti.pc, instructed by DeLaviña, state that every simple connected graph G with minimum degree δ and leaf number L(G) such that δ≥12(L(G)+1), is traceable. Here, we prove a sufficient condition for a graph to be traceable based on minimum degree and leaf number, by settling completely, the Conjecture Graffiti.pc 190. We construct infinite graphs to show that our results are best in a sense. All graphs considered are simple. That is, they neither have loops nor multiple edges.