Coloring of lattices

Mathematica Slovaca

M. Pawar¹  S. Nimbhokar¹  M. Wasadikar¹ 

关键词: coloring of a lattice;    clique number;    chromatic number;    atom;    atomic lattice;    complemented lattice;    annihilator;    ideal;   

DOI  :  10.2478/s12175-010-0022-x

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

The concept of coloring is studied for graphs derived from lattices with 0. It is shown that, if such a graph is derived from an atomic or distributive lattice, then the chromatic number equals the clique number. If this number is finite, then in the case of a distributive lattice, it is determined by the number of minimal prime ideals in the lattice. An estimate for the number of edges in such a graph of a finite lattice is given.

【 授权许可】

Unknown