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

6       nauty-cubhamg - find hamiltonian cycles in subcubic graphs
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SYNOPSIS

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

13              Pick those inputs that are nonhamiltonian and have max degree <=
14              3.
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16              infile  is  the  name of the input file in graph6/sparse6 format
17              (default: stdin)
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19              outfile is the name of  the  output  file  in  the  same  format
20              (default: stdout)
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22              The  output file will have a header >>graph6<< or >>sparse6<< if
23              the input file does.
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OPTIONS

26       -#     A parameter useful for tuning (default 100)
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28       -v     Report nonhamiltonian graphs and noncubic graphs
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30       -V     .. in addition give a cycle for the hamiltonian ones
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32       -n#-#  If the two numbers are v and i, then the i-th edge out of vertex
33              v  is  required  to be not in the cycle.  It must be that i=1..3
34              and v=0..n-1.
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36       -y#-#  If the two numbers are v and i, then the i-th edge out of vertex
37              v  is  required  to be in the cycle.  It must be that i=1..3 and
38              v=0..n-1.  You can use any number of  -n/-y  switches  to  force
39              edges.   Out of range first arguments are ignored.  If -y and -n
40              give same edge, -y wins.
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42       -i     Test + property: for each edge e, there is a  hamiltonian  cycle
43              using e.
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45       -I     Test ++ property: for each pair of edges e,e', there is a hamil‐
46              tonian cycle which uses both e and e'.
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48       -o     Test - property: for each edge e, there is a  hamiltonian  cycle
49              avoiding e.
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51       -x     Test +- property: for each pair of edges e,e', there is a hamil‐
52              tonian cycle which uses e but avoids e'.
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54       -e     Test 3/4 property: for each edge e, at least 3 of the 4 paths of
55              length 3 passing through e lie on hamiltonian cycles.
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57       -E     Test  3/4+  property:  for each edge e failing the 3/4 property,
58              all three ways of joining e to the rest of the graph are  hamil‐
59              tonian avoiding e.
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61       -T#    Specify  a  timeout, being a limit on how many search tree nodes
62              are made.  If the timeout occurs, the graph is  written  to  the
63              output as if it is nonhamiltonian.
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65       -R#    Specify the number of repeat attempts for each stage.
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67       -F     Analyze covering paths from 2 or 4 vertices of degree 2.
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69       -b     Require biconnectivity
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71       -t     Require triconnectivity  (note: quadratic algorithm)
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73   Comments:
74       -y, -n, -#, -R and -T are ignored for -i, -I, -x, -o, -e, -E, -F
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78nauty 2.6.12                     October 2019                 NAUTY-CUBHAMG(1)
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