# nauty-cubhamg - Man Page

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

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.

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