Displaying similar documents to “Minimal paths on ordered graphs”

Ordered and linked chordal graphs

Thomas Böhme, Tobias Gerlach, Michael Stiebitz (2008)

Discussiones Mathematicae Graph Theory

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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...

Efficient algorithms for minimal disjoint path problems on chordal graphs

C.P. Gopalakrishnan, C.R. Satyan, C. Pandu Rangan (1995)

Discussiones Mathematicae Graph Theory

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Disjoint paths have applications in establishing bottleneck-free communication between processors in a network. The problem of finding minimum delay disjoint paths in a network directly reduces to the problem of finding the minimal disjoint paths in the graph which models the network. Previous results for this problem on chordal graphs were an O(|V| |E|²) algorithm for 2 edge disjoint paths and an O(|V| |E|) algorithm for 2 vertex disjoint paths. In this paper, we give an O(|V| |E|)...

On k -ordered bipartite graphs.

Faudree, Jill R., Gould, Ronald J., Pfender, Florian, Wolf, Allison (2003)

The Electronic Journal of Combinatorics [electronic only]

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