A Note on $\mathtt{V}$-free 2-matchings

Kristóf Bérczi, Attila Bernáth, Máté Vizer


Motivated by a conjecture of Liang, 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.


Antimagic labelling; Hypergraph matching

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