Please help with the following problem. For part a, it seems like a greedy solution would work? Please give pseudocode.

Given a graph G = (V,E) a k-coloring of the graph is a labeling of the vertices with the colors c1, c2,..,ck such that for every edge (u,v) the color of the u is different from the color of v.

a. Give a linear time algorithm that finds a 2-coloring for a tree. b. Think about coloring a tree with 2 colors so that you have the max number of nodes colored c1. Prove that the algorithm in part (a)-with a minor modification probably-can be used to solve this problem.