Isomorph-free generation of 2-connected graphs with applications
نویسنده
چکیده
Many interesting graph families contain only 2-connected graphs, which have ear decompositions. We develop a technique to generate families of unlabeled 2-connected graphs using ear augmentations and apply this technique to two problems. In the first application, we search for uniquely Kr-saturated graphs and find the list of uniquely K4-saturated graphs on at most 12 vertices, supporting current conjectures for this problem. In the second application, we verify the Edge Reconstruction Conjecture for all 2-connected graphs on at most 12 vertices. This technique can be easily extended to more problems concerning 2-connected graphs.
منابع مشابه
EarSearch User Guide
The Ear Search program implements isomorph-free generation of 2-connected graphs by ear augmentations. This document describes the interfaces used for customized searches, as well as describes three example searches: unique saturation, edge reconstruction, and extremal graphs with a fixed number of perfect matchings.
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