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
A characterization of absolute retracts of n-chromatic graphs
β Scribed by Erwin Pesch; Werner Poguntke
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 301 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
A recursive characterization of the absolute retracts in the class of n-chromatic (connected) graphs is given.
π SIMILAR VOLUMES
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
Let n, 2 n2 L . . B n, 2 2 be integers. We say that G has an (n,, n2, , . , , n,)-chromatic factorization if G can be edge-factored as G, @ G2 @ + . . @ G, with x ( G , ) = n,, for i = 1,2, . . . , k . The following results are proved : then K,, has an (n,, n2,, . , , n,)-chromatic factorization. W
The n-component graph of a graph G is the intersection graph having a point corresponding to each n-component of G and a line joining two points whenever the corresponding n-components of G share at least one point. We give a characterization of graphs which are n-component graphs of some graph, thu
## Abstract Assuming certain conditions on a class \documentclass{article}\usepackage{amssymb,amsmath,mathrsfs}\begin{document}\pagestyle{empty}$\mathscr{C}$\end{document} of finitely generated firstβorder structures admitting the modelβtheoretical construction of a FraΓ―ssΓ© limit, we characterize r