import { TestEdge, TestGraph, TestNode } from '../generation/generators/types';
import { PropertyValidationResult } from './types';
/**
 * Validate that a graph has treewidth ≤ specified bound.
 *
 * Treewidth measures how "tree-like" a graph is:
 * - Trees and forests have treewidth 0
 * - Series-parallel graphs have treewidth ≤ 2
 * - k-trees have treewidth exactly k
 *
 * This function uses an approximation algorithm based on:
 * 1. Finding a elimination ordering
 * 2. Computing the maximum clique size in the filled graph
 * 3. Treewidth = max_clique_size - 1
 *
 * @param graph - Test graph to validate
 * @returns PropertyValidationResult with treewidth validation
 */
export declare const validateTreewidth: (graph: TestGraph) => PropertyValidationResult;
/**
 * Find the size of the maximum clique in a graph.
 *
 * A clique is a complete subgraph where all vertices are connected.
 * This uses the Bron-Kerbosch algorithm with pivot for efficiency.
 *
 * Time complexity: O(3^(n/3)) for n vertices
 *
 * @param nodes - Graph nodes
 * @param edges - Graph edges
 * @param directed - Whether graph is directed
 * @param _directed
 * @returns Size of maximum clique
 */
export declare const findMaxCliqueSize: (nodes: TestNode[], edges: TestEdge[], _directed: boolean) => number;
//# sourceMappingURL=treewidth-validator.d.ts.map