mycielskian(G, iterations=1)
The Mycielskian of graph preserves a graph's triangle free property while increasing the chromatic number by 1.
The Mycielski Operation on a graph, $G=(V, E)$ , constructs a new graph with $2|V| + 1$ nodes and $3|E| + |V|$ edges.
The construction is as follows:
Let $V = {0, ..., n-1}$
. Construct another vertex set $U = {n, ..., 2n}$
and a vertex, :None:None:`w`. Construct a new graph, M, with vertices $U \bigcup V \bigcup w$
. For edges, $(u, v) \in E$
add edges $(u, v), (u, v + n)$
, and $(u + n, v)$
to M. Finally, for all vertices $u \in U$
, add edge $(u, w)$
to M.
The Mycielski Operation can be done multiple times by repeating the above process iteratively.
More information can be found at https://en.wikipedia.org/wiki/Mycielskian
Graph, node, and edge data are not necessarily propagated to the new graph.
A simple, undirected NetworkX graph
The number of iterations of the Mycielski operation to perform on G. Defaults to 1. Must be a non-negative integer.
The Mycielskian of G after the specified number of iterations.
Returns the Mycielskian of a simple, undirected graph G
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