Clique trees of infinite locally finite chordal graphs

2013/11/27 by Christoph Hofer-Temmel, Florian Lehner, Hofer-Temmel, Christoph +1 · 2 citations
Mathematics · #05C05 05C30 #05C62 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C05 #msc:05C30 #msc:05C62

paper · pdf · doi:10.48550/arxiv.1311.7001

arxiv created 2018/03/22 · arxiv updated 2018/03/23

Abstract

We investigate clique trees of infinite locally finite chordal graphs. Our main contribution is a bijection between the set of clique trees and the product of local finite families of finite trees. Even more, the edges of a clique tree are in bijection with the edges of the corresponding collection of finite trees. This allows us to enumerate the clique trees of a chordal graph and extend various classic characterisations of clique trees to the infinite setting.

Cited by

• The global structure of locally chordal graphs
• Canonical tree-decompositions of chordal graphs

Related

• Canonical tree-decompositions of chordal graphs
• Boundary cliques, clique trees and perfect sequences of maximal cliques of a chordal graph
• The global structure of locally chordal graphs
• Clique Polynomials and Chordal Graphs
• Reduced clique graphs: a correction to "Chordal graphs and their clique graphs"