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

TL;DR

This paper investigates the labeled packing problem for (n, n-2)-graphs, providing a new lower bound on the labeled packing number into complete graphs, improving previous bounds.

Contribution

It introduces a tighter lower bound on the labeled packing number for (n, n-2)-graphs into complete graphs, advancing understanding of labeled graph packing.

Findings

Established a new lower bound for labeled packing number

Improved upon previous bounds by Woźniak

Focuses on (n, n-2)-graphs in complete graphs

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}.