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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.
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Tractably Partitioning the possible vertex k-colorings of a graph by local stability and ins...
If you limit it to specific classes of graphs, say for example star graphs, you can come up with some answers. For a star graph $S_m$, with a vertex at the center and $m$ vertices connected to the ce …