.\" DO NOT MODIFY THIS FILE!  It was generated by help2man 1.49.3.
.TH NAUTY-CUBHAMG "1" "April 2024" "nauty 2.8.8" "Nauty Manual"
.SH NAME
nauty-cubhamg \- find hamiltonian cycles in subcubic graphs
.SH SYNOPSIS
.B cubhamg
[\fI\,-#\/\fR] [\fI\,-v|-V\/\fR] [\fI\,-n#-#|-y#-#|-i|-I|-o|-O|-x|-e|-E\/\fR] [\fI\,-b|-t\/\fR] [\fI\,infile \/\fR[\fI\,outfile\/\fR]]
.SH DESCRIPTION
.IP
cubhamg : Find hamiltonian cycles in sub\-cubic graphs
.IP
infile is the name of the input file in graph6/sparse6 format
outfile is the name of the output file in the same format
.IP
stdin and stdout are the defaults for infile and outfile
.IP
The output file will have a header
if and only if the input file does.
.IP
Optional switches:
.TP
\-#
A parameter useful for tuning (default 100)
.TP
\fB\-v\fR
Report nonhamiltonian graphs and noncubic graphs
.TP
\fB\-V\fR
\&.. in addition give a cycle for the hamiltonian ones
.IP
(with \fB\-c\fR, give count for each input)
.TP
\fB\-n\fR#\-#
If the two numbers are v and i, then the i\-th edge
.IP
out of vertex v is required to be not in the cycle.
It must be that i=1..3 and v=0..n\-1.
.TP
\fB\-y\fR#\-#
If the two numbers are v and i, then the i\-th edge
.IP
out of vertex v is required to be in the cycle.
It must be that i=1..3 and v=0..n\-1.
.IP
You can use any number of \fB\-n\fR/\-y switches to force edges.
Out of range first arguments are ignored.
If \fB\-y\fR and \fB\-n\fR specify the same edge, \fB\-y\fR wins.
.TP
\fB\-i\fR
Test + property: for each edge e, there is a hamiltonian
.IP
cycle using e.
.TP
\fB\-I\fR
Test ++ property: for each pair of edges e,e', there is
.IP
a hamiltonian cycle which uses both e and e'.
.TP
\fB\-o\fR
Test \- property: for each edge e, there is a hamiltonian
.IP
cycle avoiding e
.TP
\fB\-O\fR
Test \fB\-\-\fR property: for each pair of nonadjacent edges e,e's,
.TP
there is a hamiltonian cycle avoiding both.
Note that
.IP
this is trivial unless the girth is at least 5.
.TP
\fB\-x\fR
Test +\- property: for each pair of edges e,e', there is
.IP
a hamiltonian cycle which uses e but avoids e'.
.TP
\fB\-e\fR
Test 3/4 property: for each edge e, at least 3 of the 4
.IP
paths of length 3 passing through e lie on hamiltonian cycles.
.TP
\fB\-E\fR
Test 3/4+ property: for each edge e failing the 3/4 property,
.IP
all three ways of joining e to the rest of the graph are
hamiltonian avoiding e.
.HP
\fB\-T\fR# Specify a timeout, being a limit on how many search tree
.TP
nodes are made.
If the timeout occurs, the graph is
.IP
written to the output as if it is nonhamiltonian.
.HP
\fB\-R\fR# Specify the number of repeat attempts for each stage.
.TP
\fB\-F\fR
Analyze covering paths from 2 or 4 vertices of degree 2.
.TP
\fB\-b\fR
Require biconnectivity
.TP
\fB\-t\fR
Require triconnectivity  (note: quadratic algorithm)
.TP
\fB\-c\fR
Count hamiltonian cycles, output count for each graph.
.IP
\fB\-V\fR, \fB\-n\fR and \fB\-y\fR can also be used. No graphs are output.
.HP
\fB\-y\fR, \fB\-n\fR, \-#, \fB\-R\fR and \fB\-T\fR are ignored for \fB\-i\fR, \fB\-I\fR, \fB\-x\fR, \fB\-o\fR, \fB\-e\fR, \fB\-E\fR, \fB\-F\fR