Reduce
… 3SAT to 3COL, showing NP-completeness of the latter.
Perform a polynomial-time reduction using the graph below.
- Add three interconnected vertices, colored 1, 2, and 3.
- For each variable, add two uncolored vertices connected to 2.
- For each clause, add one Or gadget connected to:
- the relevant variable vertices and
- the vertex colored 1.
Given
connect the graph
For example,
reduces to the graph