nauty-cubhamg man page
nauty-cubhamg — find hamiltonian cycles in subcubic graphs
Pick those inputs that are nonhamiltonian and have max degree <= 3.
infile is the name of the input file in graph6/sparse6 format (default: stdin)
outfile is the name of the output file in the same format (default: stdout)
The output file will have a header >>graph6<< or >>sparse6<< if the input file does.
- A parameter useful for tuning (default 100)
- Report nonhamiltonian graphs and noncubic graphs
- .. in addition give a cycle for the hamiltonian ones
- If the two numbers are v and i, then the i-th edge out of vertex v is required to be not in the cycle. It must be that i=1..3 and v=0..n-1.
- If the two numbers are v and i, then the i-th edge out of vertex v is required to be in the cycle. It must be that i=1..3 and v=0..n-1. You can use any number of -n/-y switches to force edges. Out of range first arguments are ignored. If -y and -n give same edge, -y wins.
- Test + property: for each edge e, there is a hamiltonian cycle using e.
- Test ++ property: for each pair of edges e,e', there is a hamiltonian cycle which uses both e and e'.
- Test - property: for each edge e, there is a hamiltonian cycle avoiding e.
- Test +- property: for each pair of edges e,e', there is a hamiltonian cycle which uses e but avoids e'.
- Test 3/4 property: for each edge e, at least 3 of the 4 paths of length 3 passing through e lie on hamiltonian cycles.
- Test 3/4+ property: for each edge e failing the 3/4 property, all three ways of joining e to the rest of the graph are hamiltonian avoiding e.
- Specify a timeout, being a limit on how many search tree nodes are made. If the timeout occurs, the graph is written to the output as if it is nonhamiltonian.
- Specify the number of repeat attempts for each stage.
- Analyze covering paths from 2 or 4 vertices of degree 2.
- Require biconnectivity
- Require triconnectivity (note: quadratic algorithm)
September 2016 nauty 2.6.7 Nauty Manual