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Clique trees of infinite locally finite chordal graphs. (English) Zbl 1391.05186
Summary: 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.

05C62 Graph representations (geometric and intersection representations, etc.)
05C05 Trees
05C30 Enumeration in graph theory
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