寻求可免费获取的图列表（含反例图）以验证简单图猜想

Great question—testing conjectures against small graphs is such a critical step, especially since those tiny graphs often hold the sneaky counterexamples no one sees coming! Here are some reliable, free resources to access curated graph lists (including all small graphs with ≤10 vertices) that’ll help you rigorously validate your idea:

• House of Graphs
  This is a community-driven database of known graphs, perfect for hunting down edge cases. You can filter graphs by vertex count, edge count, specific properties (like regularity, planarity, or chromatic number), and even search for graphs that match custom criteria. It lets you download graphs in multiple formats (adjacency matrices, edge lists, GraphML) which are easy to import into most graph analysis tools.

• NetworkX’s Built-in Graph Atlas
  If you’re comfortable with Python, NetworkX has a built-in generator graph_atlas_g() that returns all undirected simple graphs with up to 7 vertices. It also includes functions to generate common special graphs (Petersen, complete, cycle, bipartite, etc.) that are frequent candidates for counterexamples. A quick snippet to get started:

  import networkx as nx
  # Iterate through all small graphs in the atlas
  for graph in nx.graph_atlas_g():
      # Test your conjecture on each graph here
      pass
  

  For larger graphs (8-10 vertices), you can find precomputed datasets compatible with NetworkX from academic repositories.

• University of Waterloo Graph Database
  This resource hosts comprehensive collections of small graphs, including all connected and disconnected simple graphs with up to 10 vertices. The graphs are organized by vertex count and property (e.g., bipartite, k-regular), and available as plain-text adjacency lists—super straightforward to parse and use in your validation scripts.

• OEIS-Linked Datasets
  Since you already referenced OEIS, many graph-related sequences (like A000088, the number of simple graphs on n vertices) link to supplementary datasets containing actual graph lists. These are often hosted on academic servers or GitHub, and include machine-readable formats for n≤10 graphs. Just check the "Links" or "Data" sections of relevant OEIS entries to find them.

Pro Tips for Testing #

• Prioritize special graph classes: Regular graphs, planar graphs, critical graphs, or complements of known graphs are far more likely to break conjectures than random graphs.
• Automate the process: Use tools like NetworkX or SageMath to write scripts that batch-test your conjecture against every graph in a dataset—this saves time and eliminates human error.

内容的提问来源于stack exchange，提问作者yberman