I read the paper of "Michael LaPlante" entitle "A polynomial time algorithm for solving clique problems" and here is my commecnt on the paper:

Author claim that have a polynomial algorithm

for Maximum Clique and K-Clique problems.

The algorithm first finds the 3-Cliques,
obviously this process is polynomial because
only n*(n-1)*(n-2) ternary relation exists.
And we can easily find whole of them in a
n^3 process. But then author wish to assemble them
to produce cliques of bigger sizes.
As I see in figure 3F , 3H, 4F, 4I I think author
only consider the case when algorithm begins to
merging, it only merges the cliques they are maximum
where when you have a graph of 100 or 1000 nodes
you may begin to mergeing but the nodes that you
merged be wrong having a bigger clique using defferent
merging process. In fact the problem is that when you
want to merge them, there are many decision points and
milions number of different merging process. Yes it is
complexity of NP-Completes! let me know if I'm wrong.
Thus the algorithm is only a greedy algorithm that finds
some cliques but dont garantee they be maximum clique or
bigger than a special number K.
In fact the algorithm is correct if you add try and error
to it but is not polynomial.

Best wishes,
Kavosh Havaledarnejad
Icarus.2012@yahoo.com