Low weight perfect matchings
The electronic journal of combinatorics, Tome 27 (2020) no. 4
Answering a question posed by Caro, Hansberg, Lauri, and Zarb, we show that for every positive integer $n$ and every function $\sigma\colon E(K_{4n})\to\{-1,1\}$ with $\sigma\left(E(K_{4n})\right)=0$, there is a perfect matching $M$ in $K_{4n}$with $\sigma(M)=0$. Strengthening the consequence of a result of Caro and Yuster, we show that for every positive integer $n$ and every function $\sigma\colon E(K_{4n})\to\{-1,1\}$ with $\left|\sigma\left(E(K_{4n})\right)\right| there is a perfect matching $M$ in $K_{4n}$ with $|\sigma(M)|\leq 2$. Both these results are best possible.
@article{10_37236_9994,
author = {Stefan Ehard and Elena Mohr and Dieter Rautenbach},
title = {Low weight perfect matchings},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {4},
doi = {10.37236/9994},
zbl = {1456.05070},
url = {http://geodesic.mathdoc.fr/articles/10.37236/9994/}
}
Stefan Ehard; Elena Mohr; Dieter Rautenbach. Low weight perfect matchings. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/9994
Cité par Sources :