Coloring Of Meet-Semilattices
Coloring Of Meet-Semilattices
复制标题
DOI：
--
复制
发表时间：
2007
期刊：
影响因子：
--
通讯作者：
S. K. Nimbhokar;M. Wasadikar;Lisa Demeyer
中科院分区：
文献类型：
--
作者：
S. K. Nimbhokar;M. Wasadikar;Lisa Demeyer
给定一个具有0的交换半群S，其中0是唯一单例理想，我们关联一个简单图Γ（S），其顶点用S中的非零元素标记。当且仅当对应的元素相乘为0时，Γ（S）中的两个顶点相邻。逆问题，即，给定一个任意简单图，它是否能与某个交换半群相联系，已被证明是一个困难的问题。本文通过研究图的补，推广了DeMeyer[3]，McKenzie和Schneider[4]关于这一问题的结果.作为文[3]的应用和推广，我们证明了每个紧连通2-流形都有一个欧拉三角剖分，这个三角剖分可以与一个零因子半群图相联系。
Given a commutative semigroup S with 0, where 0 is the unique singleton ideal, we associate a simple graph Γ(S), whose vertices are labeled with the nonzero elements in S. Two vertices in Γ(S) are adjacent if and only if the corresponding elements multiply to 0. The inverse problem, i.e., given an arbitrary simple graph, whether or not it can be associated to some commutative semigroup, has proved to be a difficult one. In this paper, we extend results by DeMeyer[3], McKenzie, and Schneider[4] on this problem by studying the complement of graphs. As an application and an extension of work in [3] we prove that every compact connected 2-manifold admits an Eulerian triangulation that can be associated to a zero divisor semigroup graph.