# Ordered and linked chordal graphs

Thomas Böhme; Tobias Gerlach; Michael Stiebitz

Discussiones Mathematicae Graph Theory (2008)

- Volume: 28, Issue: 2, page 367-373
- ISSN: 2083-5892

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topThomas Böhme, Tobias Gerlach, and Michael Stiebitz. "Ordered and linked chordal graphs." Discussiones Mathematicae Graph Theory 28.2 (2008): 367-373. <http://eudml.org/doc/270596>.

@article{ThomasBöhme2008,

abstract = {
A graph G is called k-ordered if for every sequence of k distinct vertices there is a cycle traversing these vertices in the given order. In the present paper we consider two novel generalizations of this concept, k-vertex-edge-ordered and strongly k-vertex-edge-ordered. We prove the following results for a chordal graph G:
(a) G is (2k-3)-connected if and only if it is k-vertex-edge-ordered (k ≥ 3).
(b) G is (2k-1)-connected if and only if it is strongly k-vertex-edge-ordered (k ≥ 2).
(c) G is k-linked if and only if it is (2k-1)-connected.
},

author = {Thomas Böhme, Tobias Gerlach, Michael Stiebitz},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {paths and cycles; connectivity; chordal graphs},

language = {eng},

number = {2},

pages = {367-373},

title = {Ordered and linked chordal graphs},

url = {http://eudml.org/doc/270596},

volume = {28},

year = {2008},

}

TY - JOUR

AU - Thomas Böhme

AU - Tobias Gerlach

AU - Michael Stiebitz

TI - Ordered and linked chordal graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2008

VL - 28

IS - 2

SP - 367

EP - 373

AB -
A graph G is called k-ordered if for every sequence of k distinct vertices there is a cycle traversing these vertices in the given order. In the present paper we consider two novel generalizations of this concept, k-vertex-edge-ordered and strongly k-vertex-edge-ordered. We prove the following results for a chordal graph G:
(a) G is (2k-3)-connected if and only if it is k-vertex-edge-ordered (k ≥ 3).
(b) G is (2k-1)-connected if and only if it is strongly k-vertex-edge-ordered (k ≥ 2).
(c) G is k-linked if and only if it is (2k-1)-connected.

LA - eng

KW - paths and cycles; connectivity; chordal graphs

UR - http://eudml.org/doc/270596

ER -

## References

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- [7] L. Ng and M. Schultz, k-ordered Hamiltonian graphs, J. Graph Theory 24 (1997) 45-57, doi: 10.1002/(SICI)1097-0118(199701)24:1<45::AID-JGT6>3.0.CO;2-J Zbl0864.05062
- [8] R. Thomas and P. Wollan, An improved linear edge bound for graph linkages, to appear in European J. Comb. Zbl1056.05091

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