/**
 * Graph Products and Related Structures
 *
 * Graph products, minor-free graphs, and specialized graph structures.
 */
/** Toughness: minimum k such that removing k vertices disconnects */
export type Toughness = {
    kind: "toughness";
    value: number;
} | {
    kind: "unconstrained";
};
/** Integrity: resilience measure based on vertex removal */
export type Integrity = {
    kind: "integrity";
    value: number;
} | {
    kind: "unconstrained";
};
/** Cage graph: (girth, degree) combination with minimal vertices */
export type Cage = {
    kind: "cage";
    girth: number;
    degree: number;
} | {
    kind: "not_cage";
} | {
    kind: "unconstrained";
};
/** Moore graph: maximum vertices for given (diameter, degree) bound */
export type MooreGraph = {
    kind: "moore";
    diameter: number;
    degree: number;
} | {
    kind: "not_moore";
} | {
    kind: "unconstrained";
};
/** Ramanujan graph: optimal expander with spectral gap property */
export type Ramanujan = {
    kind: "ramanujan";
    degree: number;
} | {
    kind: "not_ramanujan";
} | {
    kind: "unconstrained";
};
/** Cartesian product G □ H */
export type CartesianProduct = {
    kind: "cartesian_product";
    leftFactors: number;
    rightFactors: number;
} | {
    kind: "not_cartesian_product";
} | {
    kind: "unconstrained";
};
/** Tensor (direct) product G × H */
export type TensorProduct = {
    kind: "tensor_product";
    leftFactors: number;
    rightFactors: number;
} | {
    kind: "not_tensor_product";
} | {
    kind: "unconstrained";
};
/** Strong product G ⊠ H */
export type StrongProduct = {
    kind: "strong_product";
    leftFactors: number;
    rightFactors: number;
} | {
    kind: "not_strong_product";
} | {
    kind: "unconstrained";
};
/** Lexicographic product G ∘ H */
export type LexicographicProduct = {
    kind: "lexicographic_product";
    leftFactors: number;
    rightFactors: number;
} | {
    kind: "not_lexicographic_product";
} | {
    kind: "unconstrained";
};
/** Minor-free: excludes specific graph minors (Kuratowski-Wagner theorem) */
export type MinorFree = {
    kind: "minor_free";
    forbiddenMinors: string[];
} | {
    kind: "not_minor_free";
} | {
    kind: "unconstrained";
};
/** Topological minor-free: excludes specific subdivisions */
export type TopologicalMinorFree = {
    kind: "topological_minor_free";
    forbiddenMinors: string[];
} | {
    kind: "not_topological_minor_free";
} | {
    kind: "unconstrained";
};
/** Complete bipartite property K_{m,n} */
export type CompleteBipartite = {
    kind: "complete_bipartite";
    m: number;
    n: number;
} | {
    kind: "not_complete_bipartite";
} | {
    kind: "unconstrained";
};
/** Eulerian circuit property (uses every edge exactly once, returns to start) */
export type Eulerian = {
    kind: "eulerian";
} | {
    kind: "semi_eulerian";
} | {
    kind: "non_eulerian";
} | {
    kind: "unconstrained";
};
/** k-vertex-connected property (cannot disconnect by removing < k vertices) */
export type KVertexConnected = {
    kind: "k_vertex_connected";
    k: number;
} | {
    kind: "unconstrained";
};
/** k-edge-connected property (cannot disconnect by removing < k edges) */
export type KEdgeConnected = {
    kind: "k_edge_connected";
    k: number;
} | {
    kind: "unconstrained";
};
/** Wheel graph property (cycle + central hub connected to all) */
export type Wheel = {
    kind: "wheel";
} | {
    kind: "not_wheel";
} | {
    kind: "unconstrained";
};
/** Grid/lattice graph property */
export type Grid = {
    kind: "grid";
    rows: number;
    cols: number;
} | {
    kind: "not_grid";
} | {
    kind: "unconstrained";
};
/** Toroidal graph property (grid on torus) */
export type Toroidal = {
    kind: "toroidal";
    rows: number;
    cols: number;
} | {
    kind: "not_toroidal";
} | {
    kind: "unconstrained";
};
/** Star graph property (one central vertex) */
export type Star = {
    kind: "star";
} | {
    kind: "not_star";
} | {
    kind: "unconstrained";
};
/** Comparability graph property (represents partial order) */
export type Comparability = {
    kind: "comparability";
} | {
    kind: "incomparability";
} | {
    kind: "unconstrained";
};
/** Interval graph property (intersection of intervals) */
export type Interval = {
    kind: "interval";
} | {
    kind: "not_interval";
} | {
    kind: "unconstrained";
};
/** Permutation graph property */
export type Permutation = {
    kind: "permutation";
} | {
    kind: "not_permutation";
} | {
    kind: "unconstrained";
};
/** Chordal graph property (no induced cycles > 3) */
export type Chordal = {
    kind: "chordal";
} | {
    kind: "non_chordal";
} | {
    kind: "unconstrained";
};
/** Perfect matching property */
export type PerfectMatching = {
    kind: "perfect_matching";
} | {
    kind: "near_perfect";
} | {
    kind: "no_perfect_matching";
} | {
    kind: "unconstrained";
};
/** k-colorable property */
export type KColorable = {
    kind: "k_colorable";
    k: number;
} | {
    kind: "bipartite_colorable";
} | {
    kind: "unconstrained";
};
/** Chromatic number property (minimum colors needed) */
export type ChromaticNumber = {
    kind: "chromatic_number";
    chi: number;
} | {
    kind: "unconstrained";
};
/** Treewidth property (how tree-like the graph is) */
export type Treewidth = {
    kind: "treewidth";
    width: number;
} | {
    kind: "unconstrained";
};
/** Branchwidth property */
export type Branchwidth = {
    kind: "branchwidth";
    width: number;
} | {
    kind: "unconstrained";
};
/** Flow network property */
export type FlowNetwork = {
    kind: "flow_network";
    source: string;
    sink: string;
} | {
    kind: "not_flow_network";
} | {
    kind: "unconstrained";
};
/** Binary tree property */
export type BinaryTree = {
    kind: "binary_tree";
} | {
    kind: "full_binary";
} | {
    kind: "complete_binary";
} | {
    kind: "not_binary_tree";
} | {
    kind: "unconstrained";
};
/** Spanning tree property */
export type SpanningTree = {
    kind: "spanning_tree";
    of: string;
} | {
    kind: "not_spanning_tree";
} | {
    kind: "unconstrained";
};
/** Tournament property (complete oriented graph) */
export type Tournament = {
    kind: "tournament";
} | {
    kind: "not_tournament";
} | {
    kind: "unconstrained";
};
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