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Discussiones Mathematicae Graph Theory 24(2) (2004)
291-301
DOI: https://doi.org/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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Received 1 October 2002
Revised 27 February 2003
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