/**
 * Helper algorithms for forbidden subgraph validation
 *
 * Implements complex graph class detection algorithms:
 * - Asteroidal triple detection (AT-free)
 * - House and hole detection (HH-free)
 * - Distance hereditary checking
 */
/**
 * Check if three vertices form an asteroidal triple.
 * An asteroidal triple is a set of three vertices such that for each pair,
 * there exists a path connecting them that avoids the neighborhood of the third.
 *
 * @param adjacency - Graph adjacency list
 * @param v1 - First vertex
 * @param v2 - Second vertex
 * @param v3 - Third vertex
 * @returns true if {v1, v2, v3} is an asteroidal triple
 */
export declare const hasAsteroidalTriple: (adjacency: Map<number, Set<number>>, v1: number, v2: number, v3: number) => boolean;
/**
 * Check if graph contains an induced cycle of length k.
 *
 * @param adjacency - Graph adjacency list
 * @param vertexSet - All vertices in graph
 * @param k - Cycle length to detect
 * @returns true if induced k-cycle exists
 */
export declare const hasInducedCycle: (adjacency: Map<number, Set<number>>, vertexSet: Set<number>, k: number) => boolean;
/**
 * Check if graph is distance hereditary.
 * A graph is distance hereditary if the distance between any two vertices
 * is the same in every connected induced subgraph containing them.
 *
 * This implementation uses the forbidden subgraph characterization:
 * Distance-hereditary graphs are exactly the graphs with no induced house,
 * hole (cycle of length >= 5), domino, or gem.
 *
 * @param adjacency - Graph adjacency list
 * @param vertexSet - All vertices in graph
 * @param _vertexSet
 * @returns true if graph is distance hereditary
 */
export declare const isDistanceHereditary: (adjacency: Map<number, Set<number>>, _vertexSet: Set<number>) => boolean;
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