# nauty-cubhamg - Man Page

find hamiltonian cycles in subcubic graphs

## Synopsis

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

## Description

Pick those inputs that are nonhamiltonian and have max degree <= 3.

infile is the name of the input file in graph6/sparse6 format (default: stdin)

outfile is the name of the output file in the same format (default: stdout)

The output file will have a header >>graph6<< or >>sparse6<< if the input file does.

## Options

-#

A parameter useful for tuning (default 100)

-v

Report nonhamiltonian graphs and noncubic graphs

-V

.. in addition give a cycle for the hamiltonian ones

-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 give 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.

-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)

### Comments

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

## Info

January 2021 nauty 2.7.1 Nauty Manual