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Motivated by a conjecture of Liang ~\cite{Liang13}, 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.
Bibtex entry:
| AUTHOR | = | {B{\'e}rczi, Krist{\'o}f and Bern{\'a}th, Attila and Vizer, M{\'a}t{\'e}}, |
| TITLE | = | {A note on V-free 2-matchings}, |
| NOTE | = | {{\tt egres.elte.hu}}, |
| INSTITUTION | = | {Egerv{\'a}ry Research Group, Budapest}, |
| YEAR | = | {2015}, |
| NUMBER | = | {QP-2015-04} |