AI 中文总结
该研究刻画了有限简单图的对称边多面体为闵可夫斯基可分解的充要条件，证明仅当图为三类完全多部图时满足该性质，其余情况不可分解。
AI 中文摘要
本文研究顶点集为[n]的有限简单图G的对称边多面体P_G^±的闵可夫斯基可分解性，具体给出了其对称边多面体为闵可夫斯基可分解的图的完整刻画，证明P_G^±是闵可夫斯基可分解的当且仅当G是三类完全多部图之一：K_n、K_{2,n-2}或K_{1,1,n-2}；即若G不属于这三类，则P_G^±是闵可夫斯基不可分解的。
英文摘要
In this paper, we study the Minkowski decomposability of symmetric edge polytopes $P_G^\pm$ of a finite simple graph $G$ on vertex set $[n]$. More precisely, we give a complete characterization of graphs whose symmetric edge polytopes are Minkowski decomposable. We prove that $P_G^\pm$ is Minkowski decomposable if and only if $G$ is one of the three complete multipartite graphs: $K_n$, $K_{2,n-2}$, or $K_{1,1,n-2}$. In other words, if $G$ does not belong to these three families, then $P_G^\pm$ is Minkowski indecomposable.
Comments11 pages, 1 figure, Lemma 4.2 has been revised
