Given a non-negative integer $j$ and a positive integer $k$, a $j$-restricted $k$-matching in a simple undirected graph is a $k$-matching, so that each of its connected components has at least $j+1$ edges. The maximum non-negative node weighted $j$-restricted $k$-matching problem was recently studied by Li who gave a polynomial-time algorithm and a min-max theorem for $0 \leqslant j < k$, and also proved the NP-hardness of the problem with unit node weights and $2 \leqslant k \leqslant j$. In this paper we derive an Edmonds–Gallai-type decomposition theorem for the $j$-restricted $k$-matching problem with $0 \leqslant j < k$, using the analogous decomposition for $k$-piece packings given by Janata, Loebl and Szabó, and give an alternative proof to the min-max theorem of Li.
@article{10_37236_7837,
author = {Yanjun Li and J\'acint Szab\'o},
title = {An {Edmonds-Gallai-type} decomposition for the \(j\)-restricted \(k\)-matching problem},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/7837},
zbl = {1439.05191},
url = {http://geodesic.mathdoc.fr/articles/10.37236/7837/}
}
TY - JOUR
AU - Yanjun Li
AU - Jácint Szabó
TI - An Edmonds-Gallai-type decomposition for the \(j\)-restricted \(k\)-matching problem
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/7837/
DO - 10.37236/7837
ID - 10_37236_7837
ER -
%0 Journal Article
%A Yanjun Li
%A Jácint Szabó
%T An Edmonds-Gallai-type decomposition for the \(j\)-restricted \(k\)-matching problem
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/7837/
%R 10.37236/7837
%F 10_37236_7837
Yanjun Li; Jácint Szabó. An Edmonds-Gallai-type decomposition for the \(j\)-restricted \(k\)-matching problem. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/7837
