• 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}
}
• Published 2006
• Computer Science, Mathematics
• Reports Math. Log.
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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Numerical list of forms Topical list of forms Models Notes References for relations between forms Bibliography Table 1 and Table 2 Subject index Author index Software.