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Feb 3, 2020 at 19:33 comment added smapers Without $C_3$ the graph would be 3-connected. And it seemed to work with 5-cliques, but you might as well take larger ones.
Feb 3, 2020 at 19:21 comment added Aaron Meyerowitz That looks good. But $C_3$ is irrelevant and I am not sure $5$ is enough.
Feb 3, 2020 at 8:53 history answered smapers CC BY-SA 4.0