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2014-09-26 06:31:29 -0600 asked a question How to list all the connected graphs with 9 vertices?

What I want to do is exactly to list all the connected graphs with 9 vertices which are also is_long_hole_free()==False, i.e., contains an induced cycle of length at least 5. But I can only list all the graphs with a given number of vertices, for example

G = GraphQuery(display_cols=['graph6'], num_vertices=2)
L = G.get_graphs_list()
graphs_list.show_graphs(L)
2014-09-20 22:13:53 -0600 asked a question How to get a list of graphs whose independence number equals to chromatic number?
  1. The smallest number of colors needed to color a graph G is called its chromatic number, and is often denoted χ(G).

  2. The independence number α(G) of a graph G is the size of the largest independent set of G.