On automorphisms of infinite graphs with forbidden subgraphs

Abstract

LexX be anm-connected infinite graph without subgraphs homeomorphic toKm, n, for somen, and let α be an automorphism ofX with at least one cycle of infinite length. We characterize the structure of α and use this characterization to extend a known result about orientation-preserving automorphisms of finite plane graphs to infinite plane graphs. In the last section we investigate the action of α on the ends ofX and show that α fixes at most two ends (Theorem 3.2).

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Seifter, N. On automorphisms of infinite graphs with forbidden subgraphs. Combinatorica 4, 351–356 (1984). https://doi.org/10.1007/BF02579147

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AMS subject classification (1980)

  • 05 C 25
  • 05 C 10