an:06873178
Zbl 1391.05186
Hofer-Temmel, Christoph; Lehner, Florian
Clique trees of infinite locally finite chordal graphs
EN
Electron. J. Comb. 25, No. 2, Research Paper P2.9, 15 p. (2018).
00401147
2018
j
05C62 05C05 05C30
graph theory; chordal graphs; infinite graphs; clique trees
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.