Hi all :')

I've recently solved 2017 Baltic BOI Day 1 #1 Political Development (D here

The algorithm to find the max clique here is as follows:

while (graph not empty):
     pick any vertex with min degree
     if the vertex and some subset of neighbors of it form a clique, check if it's larger than the ones we found so far
     remove the vertex

But I propose an alternate solution to finding max clique:

while (graph not empty):
     pick any vertex with min degree
     if the vertex and all neighbors of it form a clique, check if it's larger than the ones we found so far
     remove the vertex

I know it's wrong (because it's a polynomial time), but every time I try to find a counterexample, I can never do so.

Can someone provide a counterexample for my 2nd algorithm to the max clique problem (or prove it, then we have P=NP!)

Thanks,

minimario