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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2017
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/1701.06404 |
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Table des matières:
- A graph $H$ is an \emph{isometric} subgraph of $G$ if $d_H(u,v)= d_G(u,v)$, for every pair~$u,v\in V(H)$. A graph is \emph{distance preserving} if it has an isometric subgraph of every possible order. A graph is \emph{sequentially distance preserving} if its vertices can be ordered such that deleting the first $i$ vertices results in an isometric subgraph, for all $i\ge1$. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length~$5$ or greater, then it is sequentially distance preserving and thus distance preserving. Next we consider the distance preserving property on graphs with a cut vertex. Finally, we define a family of non-distance preserving graphs constructed from cycles.