NPComplete

What is the Graph Coloring Problem?

Graph coloring assigns a label, or color, to every vertex of a graph so that no two adjacent vertices share the same color, and the goal is usually to do it wi…

What is the Hamiltonian Path Problem?

A Hamiltonian path is a path through a graph that visits every vertex exactly once, and finding one (or deciding one exists) is NP-complete in general, solved…

What Does NP-Complete Mean?

A problem is NP-complete if it is in NP — meaning a proposed solution can be verified in polynomial time — and it is NP-hard, meaning every other problem in NP…

What is the P vs NP Problem?

P vs NP asks whether every problem whose solution can be verified quickly (in polynomial time, the class NP) can also be solved quickly from scratch (in polyno…

What is the Difference Between NP-Hard and NP-Complete?

NP-hard problems are at least as hard as every problem in NP, meaning any NP problem can be reduced to them in polynomial time, but they need not themselves be…