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Clique Trees of Infinite Locally Finite Chordal Graphs
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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.
The Electronic Journal of Combinatorics
Title: Clique Trees of Infinite Locally Finite Chordal Graphs
Description:
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.
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