# Graphs with small additive stretch number

Discussiones Mathematicae Graph Theory (2004)

- Volume: 24, Issue: 2, page 291-301
- ISSN: 2083-5892

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topDieter Rautenbach. "Graphs with small additive stretch number." Discussiones Mathematicae Graph Theory 24.2 (2004): 291-301. <http://eudml.org/doc/270368>.

@article{DieterRautenbach2004,

abstract = {The additive stretch number $s_\{add\}(G)$ 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 $s_\{add\}(G) ≤ k$ for some k ∈ N₀ = 0,1,2,.... Furthermore, we derive characterizations of these classes for k = 1 and k = 2.},

author = {Dieter Rautenbach},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {stretch number; distance hereditary graph; forbidden induced subgraph; forbidden subgraph},

language = {eng},

number = {2},

pages = {291-301},

title = {Graphs with small additive stretch number},

url = {http://eudml.org/doc/270368},

volume = {24},

year = {2004},

}

TY - JOUR

AU - Dieter Rautenbach

TI - Graphs with small additive stretch number

JO - Discussiones Mathematicae Graph Theory

PY - 2004

VL - 24

IS - 2

SP - 291

EP - 301

AB - The additive stretch number $s_{add}(G)$ 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 $s_{add}(G) ≤ k$ for some k ∈ N₀ = 0,1,2,.... Furthermore, we derive characterizations of these classes for k = 1 and k = 2.

LA - eng

KW - stretch number; distance hereditary graph; forbidden induced subgraph; forbidden subgraph

UR - http://eudml.org/doc/270368

ER -

## 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: 10.1007/3-540-40064-8₁0.
- [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: 10.1007/3-540-45477-2₈.
- [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. Zbl0965.05040
- [5] E. Howorka, Distance hereditary graphs, Quart. J. Math. Oxford 2 (1977) 417-420, doi: 10.1093/qmath/28.4.417. Zbl0376.05040
- [6] D. Rautenbach, A proof of a conjecture on graphs with bounded induced distance, manuscript (2002).

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