A Note on a Conjecture of Hansen Et Al
نویسندگان
چکیده
Conjecture number 747 of Graffiti (circa 1992) states that the average distance of a simple, connected graph is not more than half the maximum order of an induced bipartite subgraph. Recently, P. Hansen et al. settled this conjecture by showing that the average distance is not more than half the maximum order of an induced forest. Moreover, they conjectured that the average distance is not more than half the maximum order of an induced linear forest. In this note, we give a partial resolution of this conjecture. Namely, we show that the average distance is less than half the maximum order of an induced linear forest, plus one-half.
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