Mycielski is a graph construction which, given a graph G on n vertices, returns a graph on 2⁢n+1 vertices. If G is triangle-free with chromatic number k, then the returned graph is triangle-free with chromatic number k+1.
P≔Graph 1: an undirected unweighted graph with 10 vertices and 15 edge(s)
G≔Graph 2: an undirected unweighted graph with 21 vertices and 55 edge(s)
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