def deck(G):
    return deck_aux(G.canonical_label().copy(immutable=True))

@cached_function
def deck_aux(G):
    result = {}
    for v in G:
        H = G.copy(immutable=False)
        H.delete_vertex(v)
        H = H.canonical_label().copy(immutable=True)
        result[H] = result.get(H, 0) + 1
    return result

def statistic(G, value_only=True):
    return statistic_aux(G.canonical_label().copy(immutable=True),
                         value_only=value_only)

@cached_function
def statistic_aux(G, value_only=True):
    """
    The size of the largest multi-subset-intersection with the deck
    of another graph.

    sage: l = [(G, statistic(G, value_only=False)) for G in graphs(4)]
    sage: view([(v, G, H, deck(G), deck(H)) for G, (v, H) in l if v == 3])

    """
    DG = deck(G)
    n = G.num_verts()
    mx = 0
    best = None
    for H in graphs(n):
        if not G.is_isomorphic(H):
            DH = deck(H)
            intersection = sum(min(DH.get(U, 0), v) for U, v in DG.items())
            if mx < intersection:
                best = H
                mx = intersection
    if value_only:
        return mx
    return mx, best