• Corpus ID: 17589687

Spanning Graphs and the Axiom of Choice

@article{Delhomm2006SpanningGA,
  title={Spanning Graphs and the Axiom of Choice},
  author={Christian Delhomm{\'e} and Marianne Morillon},
  journal={Reports Math. Log.},
  year={2006},
  volume={40},
  pages={165-180}
}
A b s t r a c t. We show in set-theory ZF that the axiom of choice is equivalent to the statement every bipartite connected graph has a spanning sub-graph omitting some complete finite bipartite graph K n,n , and in particular it is equivalent to the fact that every connected graph has a spanning cycle-free graph (possibly non connected). We consider simple undirected loop-free graphs. A forest is a graph with no cycles, a tree is a connected forest. A graph G is a sub-graph of G if all its… 
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