A Counterexample to the Reconstruction Conjecture for Locally Finite Trees
نویسنده
چکیده
Two graphs G and H are hypomorphic if there exists a bijection φ : V (G)→ V (H) such that G− v ∼= H − φ(v) for each v ∈ V (G). A graph G is reconstructible if H ∼= G for all H hypomorphic to G. It is well known that not all infinite graphs are reconstructible. However, the Harary-Schwenk-Scott Conjecture from 1972 suggests that all locally finite trees are reconstructible. In this paper, we construct a counterexample to the Harary-SchwenkScott Conjecture. Our example also answers three further questions of NashWilliams and Halin on the reconstruction of infinite graphs.
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