Geodesic
Graphs with small additive stretch number
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 291-301.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: stretch number, distance hereditary graph, forbidden induced subgraph 
@article{DMGT_2004_24_2_a10,
     author = {Rautenbach, Dieter},
     title = {Graphs with small additive stretch number},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {291--301},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a10/}
}
TY  - JOUR
AU  - Rautenbach, Dieter
TI  - Graphs with small additive stretch number
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2004
SP  - 291
EP  - 301
VL  - 24
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a10/
LA  - en
ID  - DMGT_2004_24_2_a10
ER  - 
%0 Journal Article
%A Rautenbach, Dieter
%T Graphs with small additive stretch number
%J Discussiones Mathematicae. Graph Theory
%D 2004
%P 291-301
%V 24
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a10/
%G en
%F DMGT_2004_24_2_a10
Rautenbach, Dieter. Graphs with small additive stretch number. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 291-301. http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a10/

[1] H.J. Bandelt and M. Mulder, Distance-hereditary graphs, J. Combin. Theory (B) 41 (1986) 182-208, doi: 10.1016/0095-8956(86)90043-2.

[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.

[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).