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.
@article{10_37236_3928,
author = {Christoph Hofer-Temmel and Florian Lehner},
title = {Clique trees of infinite locally finite chordal graphs},
journal = {The electronic journal of combinatorics},
year = {2018},
volume = {25},
number = {2},
doi = {10.37236/3928},
zbl = {1391.05186},
url = {http://geodesic.mathdoc.fr/articles/10.37236/3928/}
}
TY - JOUR
AU - Christoph Hofer-Temmel
AU - Florian Lehner
TI - Clique trees of infinite locally finite chordal graphs
JO - The electronic journal of combinatorics
PY - 2018
VL - 25
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.37236/3928/
DO - 10.37236/3928
ID - 10_37236_3928
ER -
%0 Journal Article
%A Christoph Hofer-Temmel
%A Florian Lehner
%T Clique trees of infinite locally finite chordal graphs
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 2
%U http://geodesic.mathdoc.fr/articles/10.37236/3928/
%R 10.37236/3928
%F 10_37236_3928
Christoph Hofer-Temmel; Florian Lehner. Clique trees of infinite locally finite chordal graphs. The electronic journal of combinatorics, Tome 25 (2018) no. 2. doi: 10.37236/3928
