Labeled embedding of (n,n-2)-graphs in their complements

Abstract

Graph packing generally deals with unlabeled graphs. In \cite{EHRT11}, the authors have introduced a new variant of the graph packing problem, called the \textit{labeled packing of a graph}. This problem has recently been studied on trees \cite{TDK13} and cycles \cite{EHRT11}. In this note, we present a lower bound on the labeled packing number of any $(n,n-2)$-graph into $K_n$. This result improves the bound given by Wo\'zniak in \cite{W94}.