#Chordal Graph Completion


    # Generate all possible subsets of additional edges

    # Check if any edge subset forms a chordal graph completion


    # Create a copy of the original graph

    # Add the edges in the subset to the copy

    # Check if the resulting graph is chordal

# Example usage
    # Example instance

    # Solve the "Chordal Graph Completion" problem

    # Print the result


if __name__ == '__main__':
    import networkx as nx
    from itertools import combinations
    def chordal_graph_completion(G, K):
        edge_subsets = []
        for k in range(K + 1):
            edge_subsets.extend(combinations(list(combinations(G.nodes(), 2)), k))
        for subset in edge_subsets:
            if is_chordal_completion(G, subset):
                return True
        return False
    def is_chordal_completion(G, edge_subset):
        completion_graph = G.copy()
        completion_graph.add_edges_from(edge_subset)
        return nx.is_chordal(completion_graph)
    if __name__ == '__main__':
        G = nx.Graph()
        G.add_edges_from([(1, 2), (2, 3), (3, 1)])
        K = 1
        result = chordal_graph_completion(G, K)
        if result:
            print("Graph can be extended to a chordal graph with at most", K, "additional edges")
        else:
            print("Graph cannot be extended to a chordal graph with at most", K, "additional edges")
