I'm seeking clarity after many failed attempts to understand a few sentences that I read from a Wikipedia page. So I'm asking here on Computer-science for better understanding.
Misconception From Wikipedia
Unless P=NP any poly-time algorithm must asymptotically be wrong on more than polynomially many of the exponentially many inputs of a certain size.Wikipedia
Why and how is that easy instances of NP-complete problems that are solved in poly-time do or don't have any consequence on the P vs NP problem?
What are the mis-conceptions if I had an algorithm that solves non-finite Easy instances of any n-size of the 3-coloring problem in O(n) time?