Labeled Embedding Of (n, n-2)-Graphs In Their Complements

Graph packing generally deals with unlabeled graphs. In [4], the authors have introduced a new variant of the graph packing problem, called the labeled packing of a graph. This problem has recently been studied on trees [M.A. Tahraoui, E. Duchêne and H. Kheddouci, Labeled 2-packings of trees, Discrete Math. 338 (2015) 816-824] and cycles [E. Duchˆene, H. Kheddouci, R.J. Nowakowski and M.A. Tahraoui, Labeled packing of graphs, Australas. J. Combin. 57 (2013) 109-126]. 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 Woźniak in [Embedding graphs of small size, Discrete Appl. Math. 51 (1994) 233-241].