# Tag Archives: Algorithms-NP Complete

## Proof that Clique Decision problem is NP-Complete | Set 2

Prerequisite: NP-Completeness, Clique problem. A clique in a graph is a set of vertices where each vertex shares an edge with every other vertex. Thus,… Read More »

## 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… Read More »

## Proof that Hamiltonian Cycle is NP-Complete

Prerequisite: NP-Completeness, Hamiltonian cycle. Hamiltonian Cycle: A cycle in an undirected graph G =(V, E) which traverses every vertex exactly once. Problem Statement:Given a graph… Read More »

## Proof that Clique Decision problem is NP-Complete

Prerequisite: NP-Completeness A clique is a subgraph of a graph such that all the vertices in this subgraph are connected with each other that is… Read More »

## Proof that Subgraph Isomorphism problem is NP-Complete

Subgraph Isomorphism Problem: We have two undirected graphs G1 and G2. The problem is to check whether G1 is isomorphic to a subgraph of G2.… Read More »

## Difference between NP hard and NP complete problem

Prerequiste: NP-Completeness NP Problem: The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic… Read More »

## Proof that vertex cover is NP complete

Prerequisite – Vertex Cover Problem, NP-Completeness Problem – Given a graph G(V, E) and a positive integer k, the problem is to find whether there… Read More »

## Algorithms | NP Complete | Question 6

Which of the following is true about NP-Complete and NP-Hard problems. (A) If we want to prove that a problem X is NP-Hard, we take… Read More »

## Algorithms | NP Complete | Question 5

Which of the following statements are TRUE? (1) The problem of determining whether there exists a cycle in an undirected graph is in P. (2)… Read More »

## Algorithms | NP Complete | Question 4

The problem 3-SAT and 2-SAT are (A) both in P (B) both NP complete (C) NP-complete and in P respectively (D) undecidable and NP-complete respectively… Read More »

## Algorithms | NP Complete | Question 3

Let X be a problem that belongs to the class NP. Then which one of the following is TRUE? (A) There is no polynomial time… Read More »

## Algorithms | NP Complete | Question 2

Let S be an NP-complete problem and Q and R be two other problems not known to be in NP. Q is polynomial time reducible… Read More »

## Algorithms | NP Complete | Question 1

Assuming P != NP, which of the following is true ? (A) NP-complete = NP (B) NP-complete P = (C) NP-hard = NP (D) P… Read More »