A note on \({\mathtt V}\)-free 2-matchings (Q727204)

Summary: Motivated by a conjecture of \textit{Y.-C. Liang} [Anti-magic labeling of graphs. National Sun Yat-sen University (PhD Thesis) (2013)], we introduce a restricted path packing problem in bipartite graphs that we call a \({\mathtt V}\)-free 2-matching. We verify the conjecture through a weakening of the hypergraph matching problem. We close the paper by showing that it is NP-complete to decide whether one of the color classes of a bipartite graph can be covered by a \({\mathtt V}\)-free 2-matching.