Is the largest clique in an octahedron is 3? I have no idea how to deal with this question. QQ
2026-03-24 23:46:33.1774395993
Cardinality of the largest clique in an octahedron
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1
The answer is yes.
Pick any face of an octahedron. This is a clique with 3 vertices.
Now, suppose that there exists a clique with 4 vertices. Fix one of these, call it $V_1$. Then, the other three vertices are exactly three vertices adjacent to $V_1$. And you can visualize that these are not adjacent each other: hence they do not form a clique.