It is proved that a split graph is an absolute retract of split graphs if and only if a partition of its vertex set into a stable set and a complete set is unique or it is a complete split graph. Three equivalent conditions for a split graph to be an absolute retract of the class of all graphs are g
Absolute reflexive retracts and absolute bipartite retracts
✍ Scribed by Hans-Jürgen Bandelt; Martin Farber; Pavol Hell
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 923 KB
- Volume
- 44
- Category
- Article
- ISSN
- 0166-218X
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A graph H is an absolute retract if for every isometric embedding h of , , into a graph G an edge-preserving map g from G to H exists such that An absolute retract is uniquely determined by its set of embeddable vertices. We may regard this set as a metric space. We also prove that a graph (finite
A recursive characterization of the absolute retracts in the class of n-chromatic (connected) graphs is given.
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