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

  • Kristóf Bérczi
  • Attila Bernáth
  • Máté Vizer
Keywords: Antimagic labelling, Hypergraph matching


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.
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