#Spanning Tree Parity Problem


    # Check if each edge in the partition satisfies the parity constraint

        # If parity is not 0 or 2, the constraint is violated

    # Check if the graph is connected


# Example usage
    # Example instance

    # Solve the "Spanning Tree Parity" problem

    # Print the result


if __name__ == '__main__':
    import networkx as nx
    def spanning_tree_parity(G, partition):
        for edges in partition:
            parity = 0
            for u, v in edges:
                if (u, v) in G.edges() or (v, u) in G.edges():
                    parity += 1
            if parity != 0 and parity != 2:
                return False
        if not nx.is_connected(G):
            return False
        return True
    if __name__ == '__main__':
        G = nx.Graph()
        G.add_edges_from([(1, 2), (2, 3), (3, 1)])
        partition = [[(1, 2), (2, 3)]]
        result = spanning_tree_parity(G, partition)
        if result:
            print("Graph has a spanning tree satisfying the parity constraints")
        else:
            print("Graph does not have a spanning tree satisfying the parity constraints")
