Abstract
Results involving automorphisms and fragments of infinite graphs are proved. In particular for a given fragmentC and a vertex-transitive subgroupG of the automorphism group of a connected graph there exists σ≠G such that σ[C] ⊂C. This proves the countable case of a conjecture of L. Babai and M. E. Watkins concerning graphs allowing a vertex-transitive torsion group action.
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References
L. Babai andM. E. Watkins, Connectivity of infinite graphs having a transitive torsion group action,Arch. Math. 34 (1980), 90–96.
R. Halin, Automorphisms and endomorphisms of infinite locally finite graphs,Abh. Math. Sem. Univ. Hamburg,39 (1973), 251–283.
H. A. Jung andM. E. Watkins, On the connectivities of finite and infinite graphs,Mh. Math.,83 (1977), 121–131.
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Dedicated to Prof. K. Wagner on his 70th birthday