NAUTY-CUBHAMG(1) Nauty Manual NAUTY-CUBHAMG(1)

# NAME¶

nauty-cubhamg - find hamiltonian cycles in subcubic graphs

# SYNOPSIS¶

cubhamg [-#] [-v|-V] [-n#-#|-y#-#|-i|-I|-o|-x|-e|-E] [-b|-t] [infile [outfile]]

# DESCRIPTION¶

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.

# OPTIONS¶

-#
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