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Reconstruction of infinite graphs
β Scribed by C.St.J.A. Nash-Williams
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 929 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
β¦ Synopsis
The paper recalls several known results concerning reconstruction and edge-reconstruction of infinite graphs, and draws attention to some possibly interesting unsolved problems.
π SIMILAR VOLUMES
We show that for every infinite, rayless graph G the following holds. If G is hypomorphic to H then G is isomorphic to an induced subgraph of H and H is isomorphic to an induced subgraph of G. This proves a conjecture of R. Halin for the class of infinite, rayless graphs and partly extends a result
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## Abstract Suppose that __G, H__ are infinite graphs and there is a bijection Ξ¨; V(G) Ξ¨ V(H) such that __G__ β ΞΎ β H β Ξ¨(ΞΎ) for every ΞΎ βΌ __V__(G). Let __J__ be a finite graph and /(Ο) be a cardinal number for each Ο β __V__(J). Suppose also that either /(Ο) is infinite for every Ο β __V__(J) or _
We prove that the degree sequence of an infinite graph is reconstructibjle from its family of vertex-deleted subgraphs. Furthermore, as another result concerning the reconstruction of infinite graphs, we prove that the number c(G) of components of an infinite graph G is re~ons~uct~b~e if there is at