On Three Conjectures of GRAFFITI

Abstract

In this paper, we consider three conjectures of the computer program GRAFFITI. Moreover, we prove that every connected graph with minimum degree $\delta$ and diameter $d_m$ contains a matching of size at least $\frac{\delta (d_m+1)}{6}$. This inequality improves one of the conjectures under the additional assumption that $\delta \ge 6$.