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)

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