Given a graph G = ( V , E ) , a K - coloring is a function c : V - gt; $ 1 , 2 , . , K ; such that c ( U ) * c ( V ) for every edge ( U , V ) { E ....

Hi, need help with the two parts of this given question, in Algorithms

Given a graph G = ( V , E ) , a K - coloring is a function c : V - > $ 1 , 2 , ... , K ; such that c ( U ) * c ( V ) forevery edge ( U , V ) { E . In other words the number 1 , 2 . .. . K represent the k colors and adjacentvertices must have different colors . The decision problem K - COLOR asks if a graph can becolored with at most K colors .a . The 2 - COLOR decision problem is in P. Describe an efficient algorithm to determine if agraph has a 2 - coloring . What is the running time of your algorithm ?"b . It is known that the 3 - COLOR decision problem is NP- complete by using a reduction fromSAT . Use the fact that 3 - COLOR is NP- complete to prove that 4 - COLOR is NP- complete .