Provided by: nauty_2.6r10+ds-1_amd64 #### 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)

-v     Report nonhamiltonian graphs and noncubic graphs

-V     .. in addition give a cycle for the hamiltonian ones

-n#-#  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.

-y#-#  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.

-i     Test + property: for each edge e, there is a hamiltonian cycle using e.

-I     Test ++ property: for each pair of edges e,e', there is a hamiltonian  cycle  which
uses both e and e'.

-o     Test - property: for each edge e, there is a hamiltonian cycle avoiding e.

-x     Test  +-  property: for each pair of edges e,e', there is a hamiltonian cycle which
uses e but avoids e'.

-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.

-E     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 nodes are  made.   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.

-F     Analyze covering paths from 2 or 4 vertices of degree 2.

-b     Require biconnectivity

-t     Require triconnectivity  (note: quadratic algorithm)