Cycles in graphs of uncountable chromatic number

Abstract

We answer a question of Erdős [1], [2] by showing that any graph of uncountable chromatic number contains an edge through which there are cycles of all (but finitely many) lengths.

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References

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Thomassen, C. Cycles in graphs of uncountable chromatic number. Combinatorica 3, 133–134 (1983). https://doi.org/10.1007/BF02579349

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AMS subject classification (1980)

  • 05 C 38
  • 05 C 15