---
name: "nauty-cubhamg"
section: "1"
platform: "linux"
package: "nauty"
version: "2.8.9+ds-1+b1"
release: "Debian 13 (Trixie)"
platforms: ["linux"]
url: "https://new.carta.tech/nauty-cubhamg"
---

# nauty-cubhamg(1)

find hamiltonian cycles in subcubic graphs

## NAME

nauty-cubhamg - 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

-

  Graphs that are not hamiltonian, or not solved, are written out 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.

-

  **-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**