论文标题
低重量完美匹配
Low Weight Perfect Matchings
论文作者
论文摘要
Answering a question posed by Caro, Hansberg, Lauri, and Zarb, we show that for every positive integer $n$ and every function $σ\colon E(K_{4n})\to\{-1,1\}$ with $σ\left(E(K_{4n})\right)=0$, there is a perfect matching $M$ in $ k_ {4n} $带有$σ（m）= 0 $。加强Caro和Yuster的结果，我们表明，对于每个正整数$ n $以及每个功能$σ\ colon e（k_ {4n}）\ to \ to \ { - 1,1 \} $，带有$ \ weft | weft | et |σ\ left（e（k_ {4n}） $ k_ {4n} $带有$ |σ（m）| \ leq 2 $。这两个结果都是最好的。
Answering a question posed by Caro, Hansberg, Lauri, and Zarb, we show that for every positive integer $n$ and every function $σ\colon E(K_{4n})\to\{-1,1\}$ with $σ\left(E(K_{4n})\right)=0$, there is a perfect matching $M$ in $K_{4n}$ with $σ(M)=0$. Strengthening a result of Caro and Yuster, we show that for every positive integer $n$ and every function $σ\colon E(K_{4n})\to\{-1,1\}$ with $\left|σ\left(E(K_{4n})\right)\right|<n^2+11n+2,$ there is a perfect matching $M$ in $K_{4n}$ with $|σ(M)|\leq 2$. Both these results are best possible.
