# Is 2 coloring problem NP-complete?

## Is 2 coloring problem NP-complete?

Since graph 2-coloring is in P and it is not the trivial language (∅ or Σ∗), it is NP-complete if and only if P=NP.

## Is vertex coloring NP-complete?

Vertex coloring of a graph is a well-known NP-complete problem, but for certain classes of graphs it can be solved in polynomial time [lo]. For example, the com- plements of transitively orientable (coTR0) graphs can be colored in 0(n4) time, where n is the number of vertices [5].

Is three colors NP-complete?

To conclude, weve shown that 3-COLOURING is in NP and that it is NP-hard by giving a reduction from 3-SAT. Therefore 3-COLOURING is NP-complete.

What is an example of an NP-complete problem?

NP-complete problem, any of a class of computational problems for which no efficient solution algorithm has been found. Many significant computer-science problems belong to this class—e.g., the traveling salesman problem, satisfiability problems, and graph-covering problems.

### Can you color a graph with two colors?

5) Bipartite Graphs: We can check if a graph is Bipartite or not by coloring the graph using two colors. If a given graph is 2-colorable, then it is Bipartite, otherwise not.

### What is the difference between NP and NP-complete?

The NP problems set of problems whose solutions are hard to find but easy to verify and are solved by Non-Deterministic Machine in polynomial time….Difference between NP-Hard and NP-Complete:

NP-hard NP-Complete
To solve this problem, it do not have to be in NP . To solve this problem, it must be both NP and NP-hard problems.

Why is NP 3 hard?

Also, for any clause Cj = (x V y V z), it cannot be that all the three literals x, y, z are False. Because in this case, the output of the OR-gadget graph for Cj has to be colored False. Hence, there exists a satisfying assignment to the 3-SAT clause. Conclusion: Therefore, 3-coloring is an NP-Complete problem.

Can NP complete problems be solved?

The NP-complete problems represent the hardest problems in NP. If some NP-complete problem has a polynomial time algorithm, all problems in NP do. Although a solution to an NP-complete problem can be verified “quickly”, there is no known way to find a solution quickly.

#### Is graph coloring NP hard?

Graph coloring is computationally hard. It is NP-complete to decide if a given graph admits a k-coloring for a given k except for the cases k ∈ {0,1,2} . However, for every k > 3, a k-coloring of a planar graph exists by the four color theorem, and it is possible to find such a coloring in polynomial time.