# Tag Archives: 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 »

## Proof that Dominant Set of a Graph is NP-Complete

Pre-requisite: Dominant Set of a Graph, NP-Complete A dominating set in a graph G = (V, E) is a subset of vertices V’ following the… Read More »

## Dominant Set of a Graph

In graph theory, a dominating set for a graph G = (V, E) is a subset D of V such that every vertex not in… 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 »

## Proof that Hamiltonian Path is NP-Complete

Prerequisite : NP-Completeness The class of languages for which membership can be decided quickly fall in the class of P and The class of languages… Read More »

## Traveling Salesman Problem (TSP) Implementation

Travelling Salesman Problem (TSP): Given a set of cities and distance between every pair of cities, the problem is to find the shortest possible route… 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 »