论文标题
图形从其抽象边缘子图poset构造图形的抽象诱导子图poset
A construction of the abstract induced subgraph poset of a graph from its abstract edge subgraph poset
论文作者
论文摘要
图的抽象诱导子图POSET是该图的诱导子图POSET的同构类别，可通过子图数数适当加权。通过考虑分别由连接的分区和边缘 - 套图的poset诱导的子图的晶格，通过类似地定义了抽象的键晶格和抽象的边缘纸poset。继续我们对这些结构的图形重建理论的发展，我们表明，如果图形没有孤立的顶点，那么它的抽象键晶格和抽象诱导的子图POSET可以由抽象的边缘纸纸块构造，除了我们表征的图形族。抽象诱导子图POSET的构造是从抽象的边缘纸片Poset概括的重建理论中众所周知的结果，该理论指出，图表的顶点甲板至少具有4个边缘，并且没有孤立的顶点可以从其边缘甲板构造。12
The abstract induced subgraph poset of a graph is the isomorphism class of the induced subgraph poset of the graph, suitably weighted by subgraph counting numbers. The abstract bond lattice and the abstract edge-subgraph poset are defined similarly by considering the lattice of subgraphs induced by connected partitions and the poset of edge-subgraphs, respectively. Continuing our development of graph reconstruction theory on these structures, we show that if a graph has no isolated vertices, then its abstract bond lattice and the abstract induced subgraph poset can be constructed from the abstract edge-subgraph poset except for the families of graphs that we characterise. The construction of the abstract induced subgraph poset from the abstract edge-subgraph poset generalises a well known result in reconstruction theory that states that the vertex deck of a graph with at least 4 edges and without isolated vertices can be constructed from its edge deck.12
