Covering and 2-degree-packing numbers in graphs

Abstract

In this paper, we give a relationship between the covering number of a simple graph $G$, $β(G)$, and a new parameter associated to $G$ which is called 2-degree-packing number of $G$, $ν_2(G)$. We prove that$$\lceil ν_{2}(G)/2\rceil\leqβ(G)\leqν_2(G)-1,$$ for any connected simple graph $G$, with $|E(G)|>ν_2(G)$, and we give a characterization of simple connected graphs which attains the inequalities.