Contractible edges in 2-connected locally finite graphs
The electronic journal of combinatorics, Tome 22 (2015) no. 2
In this paper, we prove that every contraction-critical 2-connected infinite graph has no vertex of finite degree and contains uncountably many ends. Then, by investigating the distribution of contractible edges in a 2-connected locally finite infinite graph $G$, we show that the closure of the subgraph induced by all the contractible edges in the Freudenthal compactification of $G$ is 2-arc-connected. Finally, we characterize all 2-connected locally finite outerplanar graphs nonisomorphic to $K_3$ as precisely those graphs such that every vertex is incident to exactly two contractible edges as well as those graphs such that every finite bond contains exactly two contractible edges.
DOI :
10.37236/4414
Classification :
05C40, 05C45, 05C63
Mots-clés : contractible edge, Hamilton cycle, outerplanar, infinite graph
Mots-clés : contractible edge, Hamilton cycle, outerplanar, infinite graph
@article{10_37236_4414,
author = {Tsz Lung Chan},
title = {Contractible edges in 2-connected locally finite graphs},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {2},
doi = {10.37236/4414},
zbl = {1327.05180},
url = {http://geodesic.mathdoc.fr/articles/10.37236/4414/}
}
Tsz Lung Chan. Contractible edges in 2-connected locally finite graphs. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4414
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