Geodesic
Hamiltonicity in locally finite graphs: two extensions and a counterexample
Karl Heuer1
1Universität Hamburg
The electronic journal of combinatorics, Tome 25 (2018) no. 3
Cet article a éte moissonné depuis la source The Electronic Journal of Combinatorics website

Voir la notice de l'article

We state a sufficient condition for the square of a locally finite graph to contain a Hamilton circle, extending a result of Harary and Schwenk about finite graphs. We also give an alternative proof of an extension to locally finite graphs of the result of Chartrand and Harary that a finite graph not containing $K^4$ or $K_{2,3}$ as a minor is Hamiltonian if and only if it is $2$-connected. We show furthermore that, if a Hamilton circle exists in such a graph, then it is unique and spanned by the $2$-contractible edges. The third result of this paper is a construction of a graph which answers positively the question of Mohar whether regular infinite graphs with a unique Hamilton circle exist.
DOI : 10.37236/6773
Classification : 05C63, 05C45
Mots-clés : infinite graphs, locally finite graphs, ends, Hamilton cycles, uniquely Hamiltonian, outerplanar

Karl Heuer  1

1 Universität Hamburg 
@article{10_37236_6773,
     author = {Karl Heuer},
     title = {Hamiltonicity in locally finite graphs: two extensions and a counterexample},
     journal = {The electronic journal of combinatorics},
     year = {2018},
     volume = {25},
     number = {3},
     doi = {10.37236/6773},
     zbl = {1393.05191},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6773/}
}
TY  - JOUR
AU  - Karl Heuer
TI  - Hamiltonicity in locally finite graphs: two extensions and a counterexample
JO  - The electronic journal of combinatorics
PY  - 2018
VL  - 25
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.37236/6773/
DO  - 10.37236/6773
ID  - 10_37236_6773
ER  - 
%0 Journal Article
%A Karl Heuer
%T Hamiltonicity in locally finite graphs: two extensions and a counterexample
%J The electronic journal of combinatorics
%D 2018
%V 25
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/6773/
%R 10.37236/6773
%F 10_37236_6773
Karl Heuer. Hamiltonicity in locally finite graphs: two extensions and a counterexample. The electronic journal of combinatorics, Tome 25 (2018) no. 3. doi: 10.37236/6773

Cité par Sources :