DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 24(2) (2004) 291-301
DOI: 10.7151/dmgt.1232

GRAPHS WITH SMALL ADDITIVE STRETCH NUMBER

Dieter Rautenbach

Forschungsinstitut für Discrete Mathematik
Lennéstr. 2, D-53113 Bonn, Germany

e-mail: rauten@or.uni-bonn.de

Abstract

The additive stretch number sadd(G) of a graph G is the maximum difference of the lengths of a longest induced path and a shortest induced path between two vertices of G that lie in the same component of G.

We prove some properties of minimal forbidden configurations for the induced-hereditary classes of graphs G with sadd(G) ≤ k for some k ∈ N0 = { 0,1,2,…}. Furthermore, we derive characterizations of these classes for k = 1 and k = 2.

Keywords: stretch number, distance hereditary graph, forbidden induced subgraph.

2000 Mathematics Subject Classification: 05C12, 05C75.

References

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[2] S. Cicerone and G. Di Stefano, Networks with small stretch number, in: 26th International Workshop on Graph-Theoretic Concepts in Computer Science (WG'00), Lecture Notes in Computer Science 1928 (2000) 95-106, doi: 10.1007/3-540-40064-8_10.
[3] S. Cicerone, G. D'Ermiliis and G. Di Stefano, (k,+)-Distance-Hereditary Graphs, in: 27th International Workshop on Graph-Theoretic Concepts in Computer Science (WG'01), Lecture Notes in Computer Science 2204 (2001) 66-77, doi: 10.1007/3-540-45477-2_8.
[4] S. Cicerone and G. Di Stefano, Graphs with bounded induced distance, Discrete Appl. Math. 108 (2001) 3-21, doi: 10.1016/S0166-218X(00)00227-4.
[5] E. Howorka, Distance hereditary graphs, Quart. J. Math. Oxford 2 (1977) 417-420, doi: 10.1093/qmath/28.4.417.
[6] D. Rautenbach, A proof of a conjecture on graphs with bounded induced distance, manuscript (2002).

Received 1 October 2002
Revised 27 February 2003