ArticleOriginal scientific text
Title
Ordered and linked chordal graphs
Authors 1, 1, 1
Affiliations
- Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany
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
Bibliography
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Pages:
367-373
Main language of publication
English
Received
2007-09-20
Accepted
2008-04-01
Published
2008
DOI: 10.7151/dmgt.1412
Exact and natural sciences