Distributive Lattice Polymorphism on Reflexive Graphs

TL;DR

This paper characterizes reflexive graphs that admit distributive lattice polymorphisms and provides a polynomial-time algorithm to recognize such graphs under certain conditions.

Contribution

It offers two new characterizations of reflexive graphs with distributive lattice polymorphisms and an efficient recognition algorithm for graphs with unique neighborhoods.

Findings

Characterizations of reflexive graphs with distributive lattice polymorphisms

Polynomial-time recognition algorithm for graphs with unique neighborhoods

Applicable to graphs where no two vertices share the same neighborhood

Abstract

In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to address the problem of recognition: for a reflexive graph G in which no two vertices have the same neighbourhood, we find a polynomial time algorithm to decide if G admits a distributive lattice polymorphism.