On the isometric embedding of arbitrary graphs into a~graph of a~given diameter possessing the metric continuation property
Diskretnyj analiz i issledovanie operacij, Tome 8 (2001) no. 3, pp. 73-80
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We prove that an arbitrary ordinary graph $G$ can be embedded as a generated subgraph into a graph $H$ of given diameter $d(H)=d\geqslant 2$ in which any two vertices lie on some diametral path. If the diameter $d(G)$ of $G$ is less than or equal to $d$, then the embedding can be achieved isometrically, that is, with preservation of the distances between the vertices in $G$.
@article{DA_2001_8_3_a4,
author = {V. A. Tashkinov},
title = {On the isometric embedding of arbitrary graphs into a~graph of a~given diameter possessing the metric continuation property},
journal = {Diskretnyj analiz i issledovanie operacij},
pages = {73--80},
publisher = {mathdoc},
volume = {8},
number = {3},
year = {2001},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/DA_2001_8_3_a4/}
}
TY - JOUR AU - V. A. Tashkinov TI - On the isometric embedding of arbitrary graphs into a~graph of a~given diameter possessing the metric continuation property JO - Diskretnyj analiz i issledovanie operacij PY - 2001 SP - 73 EP - 80 VL - 8 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/DA_2001_8_3_a4/ LA - ru ID - DA_2001_8_3_a4 ER -
%0 Journal Article %A V. A. Tashkinov %T On the isometric embedding of arbitrary graphs into a~graph of a~given diameter possessing the metric continuation property %J Diskretnyj analiz i issledovanie operacij %D 2001 %P 73-80 %V 8 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/DA_2001_8_3_a4/ %G ru %F DA_2001_8_3_a4
V. A. Tashkinov. On the isometric embedding of arbitrary graphs into a~graph of a~given diameter possessing the metric continuation property. Diskretnyj analiz i issledovanie operacij, Tome 8 (2001) no. 3, pp. 73-80. http://geodesic.mathdoc.fr/item/DA_2001_8_3_a4/