有界简单格的不可比图的亏格

Genus of the Incomparability Graph of a Bounded Simple Lattice

一个格的不可比图以它的除最大元和最小元外的元素为顶点,两个不同的顶点相连当且仅当两者不可比.该文确定了不可比图的亏格分别为0,1,2的有界简单格的结构.

The incomparability graph of a lattice L is a graph whose vertices are the elements of L other than 0 and 1,and two distinct vertices are adjacent if and only if they are incomparable.In this paper,we mainly study the genus of incomparability graphs of simple lattices with bounded,and completely determine the structure of simple lattices with bounded whose incomparability graphs have genus 0,1,and 2,respectively.