## table of contents

NAUTY-CUBHAMG(1) | Nauty Manual | NAUTY-CUBHAMG(1) |

# NAME¶

nauty-cubhamg - 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**

July 2022 | nauty 2.7.4 |