A note on fragments of infinite graphs

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

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    L. Babai andM. E. Watkins, Connectivity of infinite graphs having a transitive torsion group action,Arch. Math. 34 (1980), 90–96.

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    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

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Jung, H.A. A note on fragments of infinite graphs. Combinatorica 1, 285–288 (1981). https://doi.org/10.1007/BF02579334

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AMS subject classification (1980)

  • 05 C 40
  • 05 C 25