论文标题
完美匹配的蜂窝图
Perfect Matching Complexes of Honeycomb Graphs
论文作者
论文摘要
图的{\ em完美匹配的复合物}是图形的边缘集上的简单复合物，其刻面与图形的完美匹配相对应。本文研究了Honeycomb图的完美匹配复合物，$ \ MATHCAL {M} _p（H_ {K \ Times M \ Times M \ Times N}）$。对于$ k = 1 $，$ \ mathcal {m} _p（h_ {1 \ times m \ times m \ times n}）$是合理的，除非$ n \ ge m = 2 $，在这种情况下，它与$（n-1）$ - sphere等于同等。另外，$ \ MATHCAL {M} _p（H_ {2 \ times 2 \ times 2}）$是同质的，等效于两个3 spheres的楔形。证明使用离散的摩尔斯理论。
The {\em perfect matching complex} of a graph is the simplicial complex on the edge set of the graph with facets corresponding to perfect matchings of the graph. This paper studies the perfect matching complexes, $\mathcal{M}_p(H_{k \times m\times n})$, of honeycomb graphs. For $k = 1$, $\mathcal{M}_p(H_{1\times m\times n})$ is contractible unless $n\ge m=2$, in which case it is homotopy equivalent to the $(n-1)$-sphere. Also, $\mathcal{M}_p(H_{2\times 2\times 2})$ is homotopy equivalent to the wedge of two 3-spheres. The proofs use discrete Morse theory.
