A Database of Graphs in Combinatorica Format

This site contains several collections of important classes of graphs, all converted to the graph format used by Combinatorica, a package for teaching and research in discrete mathematics, particularly combinatorics and graph theory. These graphs can be used to test conjectures, by explictly testing whether a given property holds on all small trees, bipartite graphs, etc. Experiments with Random labeled graphs are typically easy to construct, but experiments with them are typically wasteful because isomorphic copies can be repeatedly generated, and unconvincing because they do not systematically look for all possible counter-examples. These graph collections represent complete sets of interesting unlabeled graphs, and permit typically testing all relevant graphs up to a non-trivial number of vertices.本网站收录了若干组针对重要图类的图集，所有数据均转换为Combinatorica（一款面向离散数学、尤其是组合数学与图论领域的教学与研究工具包）所采用的图格式。此类图集可用于验证猜想，具体手段为显式检测给定性质是否在所有小型树、二分图等图类上成立。随机标号图的实验通常易于搭建，但这类实验往往冗余低效：不仅会重复生成同构图副本，且无法系统遍历所有可能的反例，因此说服力不足。这些图集均为完整的有趣无标号图集，通常可用于对顶点数不超过非平凡规模的所有相关图开展验证测试。

搜集汇总

背景与挑战

背景概述

该数据集以Combinatorica软件包格式存储了多种重要图类的完整集合，包括树、二分图等。它专为测试图论猜想而设计，通过提供无标记图的系统集合，避免了随机图测试中的同构重复问题，并能覆盖非平凡顶点数的所有相关图。