The distinguishing number and distinguishing chromatic number for posets

2019/05/23 by Collins, Karen L., Trenk, Ann N. · 1 citation
#05 #06 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.09858

Abstract

In this paper we introduce the concepts of the distinguishing number and the distinguishing chromatic number of a poset. For a distributive lattice L and its set Q_L of join-irreducibles, we use classic lattice theory to show that any linear extension of Q_L generates a distinguishing 2-coloring of L. We prove general upper bounds for the distinguishing chromatic number and particular upper bounds for the Boolean lattice and for divisibility lattices. In addition, we show that the distinguishing number of any twin-free Cohen-Macaulay planar lattice is at most 2.

Cited by

• Breaking the Symmetries of Amenable Graphs

Related

• Distinguishing Number of Countable Homogeneous Relational Structures
• The distinguishing chromatic number of bipartite graphs of girth at least six
• Poset Ramsey Number R(P,Q_n). II. Antichains
• Poset Ramsey number R(P,Q_n). III. Chain Compositions and Antichains
• On colorings of the Boolean lattice avoiding a rainbow copy of a poset