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

13              cubhamg : Find hamiltonian cycles in sub-cubic graphs
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15              infile is the name of the input file  in  graph6/sparse6  format
16              outfile is the name of the output file in the same format
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18              stdin and stdout are the defaults for infile and outfile
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20              The output file will have a header if and only if the input file
21              does.
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23              Optional switches:
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25       -#     A parameter useful for tuning (default 100)
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27       -v     Report nonhamiltonian graphs and noncubic graphs
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29       -V     .. in addition give a cycle for the hamiltonian ones
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31              (with -c, give count for each input)
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33       -n#-#  If the two numbers are v and i, then the i-th edge
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35              out of vertex v is required to be not in the cycle.  It must  be
36              that i=1..3 and v=0..n-1.
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38       -y#-#  If the two numbers are v and i, then the i-th edge
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40              out of vertex v is required to be in the cycle.  It must be that
41              i=1..3 and v=0..n-1.
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43              You can use any number of -n/-y switches to force edges.  Out of
44              range  first  arguments  are  ignored.  If -y and -n specify the
45              same edge, -y wins.
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47       -i     Test + property: for each edge e, there is a hamiltonian
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49              cycle using e.
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51       -I     Test ++ property: for each pair of edges e,e', there is
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53              a hamiltonian cycle which uses both e and e'.
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55       -o     Test - property: for each edge e, there is a hamiltonian
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57              cycle avoiding e
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59       -O     Test -- property: for each pair of nonadjacent edges e,e's,
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61       there is a hamiltonian cycle avoiding both.
62              Note that
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64              this is trivial unless the girth is at least 5.
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66       -x     Test +- property: for each pair of edges e,e', there is
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68              a hamiltonian cycle which uses e but avoids e'.
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70       -e     Test 3/4 property: for each edge e, at least 3 of the 4
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72              paths of length 3 passing through e lie on hamiltonian cycles.
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74       -E     Test 3/4+ property: for each edge e failing the 3/4 property,
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76              all three ways of joining e to the rest of the graph are  hamil‐
77              tonian avoiding e.
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79       -T# Specify a timeout, being a limit on how many search tree
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81       nodes are made.
82              If the timeout occurs, the graph is
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84              written to the output as if it is nonhamiltonian.
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86       -R# Specify the number of repeat attempts for each stage.
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88       -F     Analyze covering paths from 2 or 4 vertices of degree 2.
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90       -b     Require biconnectivity
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92       -t     Require triconnectivity  (note: quadratic algorithm)
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94       -c     Count hamiltonian cycles, output count for each graph.
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96              -V, -n and -y can also be used. No graphs are output.
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98       -y, -n, -#, -R and -T are ignored for -i, -I, -x, -o, -e, -E, -F
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102nauty 2.8.8                      November 2023                NAUTY-CUBHAMG(1)