Adding Vertex with Arraylist

I am trying to vertex to 2 arraylist ( setA, setB) in which I am going to store vertices. Later on I am going to compare them using BFS and find the Maximam Size(Bipartite Graph) but i am stuck on getting the input.

here is what i have so far

import java.util.*;



public class BipartiteGraph {

    private String strName;
    ArrayList<Vertex>[] vertexList;

    public BipartiteGraph(){

        vertexList = new ArrayList[2];
        vertexList[0] = new ArrayList<Vertex>();
        vertexList[1] = new ArrayList<Vertex>();
    }

    public boolean setA(Vertex v1){
        vertexList[0].add(v1);
        return false;
    }

    public boolean setB(Vertex v2){
        vertexList[1].add(v2);
        return false;
    }  
}

class Vertex{
    public String name;   
    public List adj; 
    public Vertex next; 
    public Vertex(String nm){
        name = nm;
        adj = new LinkedList();
      }
}

class Edge{
    public Vertex vertA;   
    public Vertex vertB;  
    public Edge( Vertex destination, Vertex comesfrom ){
        vertA = comesfrom;
        vertB = destination;
    }

    public static void main(String[] args){
      Scanner vertexInput = new Scanner(System.in);
      BipartiteGraph g = new BipartiteGraph( );
      g.setA(vertexInput.nextBoolean()); <-- I get the error here and to resolve it I tried new Vertex(.....) but that did not work as well
    } 
}

How can i take the input correctly so that i can perform BFS search late. Also I need to use adjacency list. Can I use it with my current code later?