use crate::Graph;

pub fn theorem3_1(g: &Graph) -> bool {
    let claw = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 1, 1],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
            vec![1, 0, 0, 0],
        ],
    };

    let z1 = Graph {
        size: 4,
        matrix: vec![
            vec![0, 1, 0, 0],
            vec![1, 0, 1, 1],
            vec![0, 1, 0, 1],
            vec![0, 1, 1, 0],
        ],
    };

    let forbidden = vec![claw, z1];

    return g.is_2_connected() && g.is_free_of(&forbidden);
}