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.
@article{10_37236_5258,
author = {Krist\'of B\'erczi and Attila Bern\'ath and M\'at\'e Vizer},
title = {A note on \({\mathtt {V}\)-free} 2-matchings},
journal = {The electronic journal of combinatorics},
year = {2016},
volume = {23},
number = {4},
doi = {10.37236/5258},
zbl = {1351.05195},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5258/}
}
TY - JOUR
AU - Kristóf Bérczi
AU - Attila Bernáth
AU - Máté Vizer
TI - A note on \({\mathtt V}\)-free 2-matchings
JO - The electronic journal of combinatorics
PY - 2016
VL - 23
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.37236/5258/
DO - 10.37236/5258
ID - 10_37236_5258
ER -
%0 Journal Article
%A Kristóf Bérczi
%A Attila Bernáth
%A Máté Vizer
%T A note on \({\mathtt V}\)-free 2-matchings
%J The electronic journal of combinatorics
%D 2016
%V 23
%N 4
%U http://geodesic.mathdoc.fr/articles/10.37236/5258/
%R 10.37236/5258
%F 10_37236_5258
Kristóf Bérczi; Attila Bernáth; Máté Vizer. A note on \({\mathtt V}\)-free 2-matchings. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/5258
