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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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Proving that every graph is an induced subgraph of an r-regular graph
Take two copies $G_1$ and $G_2$ of $G$ and add and edge between each vertex $v$ of $G_1$ and every vertex of $G_2$ corresponding to non-neighbours of $v$. Then $G$ is obviously an induced subgraph, th …