## ORDERED AND LINKED CHORDAL GRAPHS

Thomas Böhme,  Tobias Gerlach and Michael Stiebitz

Institut für Mathematik
Technische Universität Ilmenau
Ilmenau, Germany
 e-mail: tboehme@theoinf.tu-ilmenau.de e-mail: tobias.gerlach@tu-ilmenau.de e-mail: stieb@mathematik.tu-ilmenau.de

## 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.

Keywords: paths and cycles, connectivity, chordal graphs.

2000 Mathematics Subject Classification: 05C38, 05C40.

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