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junkawahara committed Sep 16, 2024
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Expand Up @@ -569,12 +569,56 @@ You can specify a graph type, such as paths and trees, and create a
GraphSet object that stores all graphs matching the type. Graphillion
supports the following graph types:

- connected components,
- cliques,
- trees,
- forests,
- cycles, and
- paths.
| Method | Description |
| :-------------------------------------------------------------------- | :----------------------------------------------------- |
| `GraphSet.graphs(constraints)` | Returns a GraphSet with graphs under given constraints |
| `GraphSet.connected_components(vertices)` | Returns a GraphSet of connected components |
| `GraphSet.cliques(k)` | Returns a GraphSet of k-cliques |
| `GraphSet.bicliques(a, b)` | Returns a GraphSet of (a, b)-bicliques |
| `GraphSet.trees(root, is_spanning)` | Returns a GraphSet of trees |
| `GraphSet.forests(roots, is_spanning)` | Returns a GraphSet of forests, sets of trees |
| `GraphSet.cycles(is_hamilton)` | Returns a GraphSet of cycles |
| `GraphSet.paths(terminal1, terminal2, is_hamilton)` | Returns a GraphSet of paths |
| `GraphSet.matchings()` | Returns a GraphSet of matchings |
| `GraphSet.perfect_matchings()` | Returns a GraphSet of perfect matchings |
| `GraphSet.k_matchings(k)` | Returns a GraphSet of k-matchings |
| `GraphSet.b_matchings(b)` | Returns a GraphSet of b-matchings |
| `GraphSet.k_factors(k)` | Returns a GraphSet of k-factors |
| `GraphSet.f_factors(f)` | Returns a GraphSet of f-factors |
| `GraphSet.regular_graphs(degree, is_connected)` | Returns a GraphSet of regular graphs |
| `GraphSet.bipartite_graphs()` | Returns a GraphSet of bipartite graphs |
| `GraphSet.regular_bipartite_graphs(degree, is_connected)` | Returns a GraphSet of regular bipartite graphs |
| `GraphSet.steiner_subgraphs(terminals)` | Returns a GraphSet of Steiner subgraphs |
| `GraphSet.steiner_trees(terminals)` | Returns a GraphSet of Steiner trees |
| `GraphSet.steiner_cycles(terminals)` | Returns a GraphSet of Steiner cycles |
| `GraphSet.steiner_paths(terminals)` | Returns a GraphSet of Steiner paths |
| `GraphSet.degree_distribution_graphs(deg_dist, is_connected)` | Returns a GraphSet of degree distribution graphs |
| `GraphSet.letter_P_graphs()` | Returns a GraphSet of 'P'-shaped graphs |
| `GraphSet.partitions(num_comp_lb, num_comp_ub)` | Returns a GraphSet of partitions |
| `GraphSet.balanced_partitions(weight_list, ratio, lower, upper, num_comps)` | Returns a GraphSet of balanced_partitions |
| `GraphSet.induced_graphs()` | Returns a GraphSet of induced graphs |
| `GraphSet.weighted_induced_graphs(weight_list, lower, upper)` | Returns a GraphSet of induced graphs with weight_list |
| `GraphSet.forbidden_induced_subgraphs()` | Returns a GraphSet of forbidden induced subgraphs |

GraphClass class supports the following further graph classes:
- claw_graphs
- claw_free_graphs
- diamond_graphs
- diamond_free_graphs
- gem_graphs
- gem_free_graphs
- odd_hole_graphs
- odd_hole_free_graphs
- chordal_graphs
- cographs
- chordal_bipartite_graphs
- split_graphs
- block_graphs
- ptolemaic_graphs
- threshold_graphs
- gridline_graphs
- domino_graphs
- linear_domino_graphs

For example, `paths()` method takes two arguments, two end vertices,
and finds all paths between the vertices.
Expand Down Expand Up @@ -611,6 +655,13 @@ graphs are selected only from the GraphSet object. Please see the
library reference for more details. The internal implementation of
`graphs()` is independently available as [TdZdd].

GraphClass class can be used as follows:

```python
from graphillion.graphclass import GraphClass
gs = GraphClass.claw_free_graphs()
```

Manipulating graphsets
--------------------------------------------------------------------------------

Expand Down Expand Up @@ -661,19 +712,27 @@ Creation methods specifying graph types also work as selection methods.
| `gs.graphs(constraints)` | Returns a GraphSet with graphs under given constraints |
| `gs.connected_components(vertices)` | Returns a GraphSet of connected components |
| `gs.cliques(k)` | Returns a GraphSet of k-cliques |
| `gs.bicliques(a, b)` | Returns a GraphSet of (a, b)-bicliques |
| `gs.trees(root, is_spanning)` | Returns a GraphSet of trees |
| `gs.forests(roots, is_spanning)` | Returns a GraphSet of forests, sets of trees |
| `gs.cycles(is_hamilton)` | Returns a GraphSet of cycles |
| `gs.paths(terminal1, terminal2, is_hamilton)` | Returns a GraphSet of paths |
| `gs.matchings()` | Returns a GraphSet of matchings |
| `gs.perfect_matchings()` | Returns a GraphSet of perfect matchings |
| `gs.partitions(num_comp_lb, num_comp_ub)` | Returns a GraphSet of partitions |
| `gs.balanced_partitions(weight_list, ratio, lower, upper, num_comps)` | Returns a GraphSet of balanced_partitions |
| `gs.induced_graphs()` | Returns a GraphSet of induced graphs |
| `gs.weighted_induced_graphs(weight_list, lower, upper)` | Returns a GraphSet of induced graphs with weight_list |
| `gs.chordal_graphs()` | Returns a GraphSet of chordal graphs |
| `gs.k_matchings(k)` | Returns a GraphSet of k-matchings |
| `gs.b_matchings(b)` | Returns a GraphSet of b-matchings |
| `gs.k_factors(k)` | Returns a GraphSet of k-factors |
| `gs.f_factors(f)` | Returns a GraphSet of f-factors |
| `gs.regular_graphs(degree, is_connected)` | Returns a GraphSet of regular graphs |
| `gs.forbidden_induced_subgraphs()` | Returns a GraphSet of forbidden induced subgraphs |
| `gs.bipartite_graphs()` | Returns a GraphSet of bipartite graphs |

| `gs.regular_bipartite_graphs(degree, is_connected)` | Returns a GraphSet of regular bipartite graphs |
| `gs.steiner_subgraphs(terminals)` | Returns a GraphSet of Steiner subgraphs |
| `gs.steiner_trees(terminals)` | Returns a GraphSet of Steiner trees |
| `gs.steiner_cycles(terminals)` | Returns a GraphSet of Steiner cycles |
| `gs.steiner_paths(terminals)` | Returns a GraphSet of Steiner paths |
| `gs.degree_distribution_graphs(deg_dist, is_connected)` | Returns a GraphSet of degree distribution graphs |
| `gs.letter_P_graphs()` | Returns a GraphSet of 'P'-shaped graphs |

### Modification or generation methods

Expand Down

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