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Minimal extensions of graphs to absolute retracts

โœ Scribed by Erwin Pesch

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
631 KB
Volume
11
Category
Article
ISSN
0364-9024

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โœฆ Synopsis

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 metric space with integral distance) can be isometrically embedded into only one smallest absolute retract (injective hull). All graphs in this paper are finite, connected, and without multiple edges.

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## Abstract For __n__ sufficiently large the order of a smallest balanced extension of a graph of order __n__ is, in the worst case, โŒŠ(__n__ + 3)^2^/8โŒ‹. ยฉ 1993 John Wiley & Sons, Inc.