Please help with this problem?

Question

Problem 1 - Triangle Problem (TRIANGLE). A triangle in an undirected graph is a
subgraph that has 3 vertexes connected to each other (so that they form a triangle). We are asked
”Given an undirected graph G, does it contain triangle?”
Is TRIANGLE in P? if not, is it in NP?
• If the problem is in P give a polynomial-time algorithm that decides it;
• If the problem is in NP, but you cannot show that it is in P give a polynomial-time verifier.

Answer 1

sure

Answer 2

This problem is in P, because if G has n vertices, then there are n(n-1)(n-2)/6 possible combinations of 3 vertices to check, and it takes O(1) time to check if any set of 3 vertices forms a triangle.