A Note on Packing Graphs Without Cycles of Length up to Five - Görlich, Agnieszka; Żak, Andrzej (The Electronic Journal of Combinatorics, 2009)
The following statement was conjectured by Faudree, Rousseau, Schelp and Schuster: if a graph G is a non-star graph without cycles of length m ≤ 4 then G is a subgraph of its complement. So far the best result concerning this conjecture is that every non-star graph G without cycles of length m ≤ 6 is a subgraph of its complement. In this note we show that m≤ 6 can be replaced by m ≤ 5.