Monochromatic triangle
Encyclopedia
The monochromatic triangle problem is a decision problem
that is known to be NP-complete
.
Input: An n-node undirected graph G(V,E) with node set V and edge set E.
Question: Can the edges, E, of G be partitioned into two disjoint sets E1 and E2, such that neither of the two graphs G1(V,E1) and G2(V,E2) contain a triangle? That is to say: for all nodes in E1 or E2 there does not exist a set {u,v,w} such that {u,v}, {u,w}, {v,w} are all edges.
Decision problem
In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters. For example, the problem "given two numbers x and y, does x evenly divide y?" is a decision problem...
that is known to be NP-complete
NP-complete
In computational complexity theory, the complexity class NP-complete is a class of decision problems. A decision problem L is NP-complete if it is in the set of NP problems so that any given solution to the decision problem can be verified in polynomial time, and also in the set of NP-hard...
.
Input: An n-node undirected graph G(V,E) with node set V and edge set E.
Question: Can the edges, E, of G be partitioned into two disjoint sets E1 and E2, such that neither of the two graphs G1(V,E1) and G2(V,E2) contain a triangle? That is to say: for all nodes in E1 or E2 there does not exist a set {u,v,w} such that {u,v}, {u,w}, {v,w} are all edges.