1. Design a polynomial-time algorithm for the graph 2-coloring problem: determine whether vertices of a given graph can be colored in no more than two colors so that no two adjacent vertices are colored the same color.
2. Consider the following brute-force algorithm for solving the composite number problem: Check successive integers from [2 to n/2] as possible divisors of n. If one of them divides n evenly, return yes (i.e., the number is composite); if none of them does, return no. Why does this algorithm not put the problem in class P?