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

              Graphs  that  are  not hamiltonian, or not solved, are written out 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)

       -v     Report nonhamiltonian graphs and noncubic graphs

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

              (with -c, give count for each input)

       -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 specify the 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

       -O     Test -- property: for each pair of nonadjacent edges e,e's,

       there is a hamiltonian cycle avoiding both.
              Note that

              this is trivial unless the girth is at least 5.

       -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)

       -c     Count hamiltonian cycles, output count for each graph.

              -V, -n and -y can also be used. No graphs are output.

       -y, -n, -#, -R and -T are ignored for -i, -I, -x, -o, -e, -E, -F

nauty 2.8.9                                      September 2024                                 NAUTY-CUBHAMG(1)