C(S_0,5) Induced Subgraph Decider

This app decides whether a given finite graph appears as an induced subgraph of the curve graph of the five-punctured sphere, C(S_0,5).

By the theorem of Aougab, Biringer, and Gaster, a finite graph embeds as an induced subgraph of a curve graph C(S) if and only if its clique number is at most the surface's complexity ξ(S). Because ξ(S_0,5) = 2, a graph embeds if and only if it is strictly triangle-free.

Input Graph (Set of pairs of vertices): { {1,2}, {1,3}, {1,4}, {2,4} } Decide Embedding