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|-O|-x|-e|-E] [-b|-t] [infile [outfile]]

# DESCRIPTION¶

cubhamg : Find hamiltonian cycles in sub-cubic graphs
infile is the name of the input file in graph6/sparse6 format outfile is the name of the output file in the same format
stdin and stdout are the defaults for infile and outfile
The output file will have a header if and only if the input file does.
Optional switches:
-#
A parameter useful for tuning (default 100)
Report nonhamiltonian graphs and noncubic graphs
.. in addition give a cycle for the hamiltonian ones
(with -c, give count for each input)
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 specify the 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 nonadjacent edges e,e's,
Note that
this is trivial unless the girth is at least 5.
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.

-T# Specify a timeout, being a limit on how many search tree

If the timeout occurs, the graph is
written to the output as if it is nonhamiltonian.

-R# Specify the number of repeat attempts for each stage.

Analyze covering paths from 2 or 4 vertices of degree 2.
Require biconnectivity