On a Problem of Cameron’s on Inexhaustible Graphs

A graph G is inexhaustible if whenever a vertex of G is deleted the remaining graph is isomorphic to G. We address a question of Cameron [6], who asked which countable graphs are inexhaustible. In particular, we prove that there are continuum many countable inexhaustible graphs with properties in common with the infinite random graph, including adjacency properties and universality. Locally finite inexhaustible graphs and forests are investigated, as is a semigroup structure on the class of inexhaustible graphs. We extend a result of [7] on homogeneous inexhaustible graphs to pseudo-homogeneous inexhaustible graphs.

This is a preview of subscription content, access via your institution.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Anthony Bonato.

Additional information

The authors gratefully acknowledge support from the Natural Science and Engineering Research Council of Canada (NSERC).

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bonato, A., Delić, D. On a Problem of Cameron’s on Inexhaustible Graphs. Combinatorica 24, 35–51 (2004). https://doi.org/10.1007/s00493-004-0003-1

Download citation

Mathematics Subject Classification (2000):

  • 05C75
  • 03C15