yozw / dbe

De Bruijn Erdos

De Bruijn-Erdős computational combinatorics

Installation and compilation

• Install Bazel.
• Install Nauty.
• Install Boost.
• Clone this repo: git clone https://github.com/yozw/dbe.git.
• Run bazel build -c opt ....
• To run unit tests: bazel test -c opt ....

Usage examples

Generate all bipartite graphs of order 5 that have no universal line:

nauty/geng -b 5 | bazel-out/g2dist | bazel-out/dbe -u | nauty/showg -A

Generate all biconnected bipartite graphs of order 5, add one vertex in any way, remove isomorphic duplicates, and find all graphs among the resulting graphs that have no universal line:

nauty/geng -b 6 | bazel-out/add_vertex | nauty/shortg | bazel-out/g2dist | bazel-out/dbe -u | nauty/showg -A

There are 172 such graphs. To impose in addition that the starting bipartite graphs are biconnected:

nauty/geng -b -C 6 | bazel-out/add_vertex | nauty/shortg | bazel-out/g2dist | bazel-out/dbe -u | nauty/showg -A

There are 69 such graphs. To output graphs that do not have n distinct lines instead:

nauty/geng -b -C 6 | bazel-out/add_vertex | nauty/shortg | bazel-out/g2dist | bazel-out/dbe -n | nauty/showg -A

Parallellizing using GNU Parallel:

nauty/geng -b -C 11 | parallel --block 10K --pipe 'bazel-out/add_vertex | nauty/shortg' | nauty/shortg | bazel-out/g2dist \
    | parallel --pipe bazel-out/dbe -n | nauty/showg -A > output.txt
nauty/geng -b -d2 11 | parallel --block 5K --pipe 'bazel-out/add_vertex | nauty/shortg' | nauty/shortg | bazel-out/g2dist \
    | parallel --block 5M --pipe bazel-out/dbe -n | nauty/showg -A > output.txt

These pipelines do the following:

• Generate a set of base graphs (all 2-connected bipartite graphs of order 11, and all bipartite graphs of order 11 with minimum degree, respectively).
• Partition that set, and for each partition do the following in parallel: take each graph and add a vertex in every possible way; then, remove isomorphic duplicates.
• Take the output from the previous stage and remove isomorphic duplicates.
• From the previous stage, find all graphs that do not have at least n (=12 in this case) distinct lines.
• Present the results in a human-readable form and write them to output.txt.

The output turns out to be empty.