In computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution.

Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the given graph.

May 15, 2024 · Proof that Independent Set in Graph theory is NP Complete Prerequisite: NP-Completeness, Independent set. An Independent Set S of graph G = (V, E) is a set of vertices such that no two vertices in S are adjacent to each other.

In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems.

Feb 22, 2025 · The NP in NP class stands for Non-deterministic Polynomial Time. It is the collection of decision problems that can be solved by a non-deterministic machine (note that our computers are deterministic) in polynomial time.

Mar 18, 2024 · Graph Theory Learn how GPS systems find the shortest routes, how engineers design integrated circuits and more real-world uses of graphs

In graph theory and computer science, NP-Complete problems are a group of problems that are very hard to solve. These problems share two important features: first, it is easy to check if a solution is correct once you have it (that's what NP means), and second, if you could solve one NP-Complete problem quickly, you could solve all NP problems ...

• Define the class NP and the notion of NP completeness, using non-deterministic Turing machines. • Prove the Cook-Levin Theorem: SAT is NP complete. • Prove that 3-SAT is NP complete. • Prove that graph 3-colorability is NP complete. • Prove that the problem of finding a maximal independent set, or a

a graph (greedily color the first vertex blue, all its neighbors red, all their neighbors blue and so on), we know of no such algorithm for 3-coloring a a graph. Theorem 1. 3COL is NP-complete. Sketch of Proof The coloring serves as a witness that can be veri-fied in polynomial time, so3COL ∈NP. Next we show how to reduce

NP is the set of all decision problems whose YES answer is checkable in polynomial-time. co-NP is the set of all decision problems whose NO answer is checkable in polynomial-time. A problem is NP-Hard iff a polynomial-time solution for it would imply a …