# On the existence of a cycle of length at least 7 in a (1,≤ 2)-twin-free graph

David Auger; Irène Charon; Olivier Hudry; Antoine Lobstein

Discussiones Mathematicae Graph Theory (2010)

- Volume: 30, Issue: 4, page 591-609
- ISSN: 2083-5892

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topDavid Auger, et al. "On the existence of a cycle of length at least 7 in a (1,≤ 2)-twin-free graph." Discussiones Mathematicae Graph Theory 30.4 (2010): 591-609. <http://eudml.org/doc/270978>.

@article{DavidAuger2010,

abstract = {We consider a simple, undirected graph G. The ball of a subset Y of vertices in G is the set of vertices in G at distance at most one from a vertex in Y. Assuming that the balls of all subsets of at most two vertices in G are distinct, we prove that G admits a cycle with length at least 7.},

author = {David Auger, Irène Charon, Olivier Hudry, Antoine Lobstein},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {undirected graph; twin subsets; identifiable graph; distinguishable graph; identifying code; maximum length cycle},

language = {eng},

number = {4},

pages = {591-609},

title = {On the existence of a cycle of length at least 7 in a (1,≤ 2)-twin-free graph},

url = {http://eudml.org/doc/270978},

volume = {30},

year = {2010},

}

TY - JOUR

AU - David Auger

AU - Irène Charon

AU - Olivier Hudry

AU - Antoine Lobstein

TI - On the existence of a cycle of length at least 7 in a (1,≤ 2)-twin-free graph

JO - Discussiones Mathematicae Graph Theory

PY - 2010

VL - 30

IS - 4

SP - 591

EP - 609

AB - We consider a simple, undirected graph G. The ball of a subset Y of vertices in G is the set of vertices in G at distance at most one from a vertex in Y. Assuming that the balls of all subsets of at most two vertices in G are distinct, we prove that G admits a cycle with length at least 7.

LA - eng

KW - undirected graph; twin subsets; identifiable graph; distinguishable graph; identifying code; maximum length cycle

UR - http://eudml.org/doc/270978

ER -

## References

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- [9] T. Laihonen, On cages admitting identifying codes, European J. Combinatorics 29 (2008) 737-741, doi: 10.1016/j.ejc.2007.02.016. Zbl1143.05036
- [10] T. Laihonen and J. Moncel, On graphs admitting codes identifying sets of vertices, Australasian J. Combinatorics 41 (2008) 81-91. Zbl1201.05072
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- [12] A. Lobstein, Bibliography on identifying, locating-dominating and discriminating codes in graphs, http://www.infres.enst.fr/~lobstein/debutBIBidetlocdom.pdf.
- [13] J. Moncel, Codes identifiants dans les graphes, Thèse de Doctorat, Université de Grenoble, France, 165 pages, June 2005.

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