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# 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

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 Ā (note: quadratic algorithm)

-c

Count hamiltonian cycles, output count for each graph.

-V, -n and -y can also be used. No graphs are output.

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

## Info

April 2024 nauty 2.8.8 Nauty Manual