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Questions about the branch of combinatorics called graph theory (not to be used for questions concerning the graph of a function). This tag can be further specialized via using it in combination with more specialized tags such as extremal-graph-theory, spectral-graph-theory, algebraic-graph-theory, topological-graph-theory, random-graphs, graph-colorings and several others.

6 votes

Non-definability of graph 3-colorability in first-order logic

It’s worth noting that Joel’s great answer says that $n$-colorability is not definable by a single sentence of first-order logic. However, it is definable by a first-order theory.. That is, for each …
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