## table of contents

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

# NAME¶

nauty-twohamg - split quartic graphs into two hamiltonian cycles

# SYNOPSIS¶

**twohamg** [*-sgvq*] [*-L#*] [*infile
*[*outfile*]]

# DESCRIPTION¶

- Partition quartic graphs into two hamiltonian cycles.
- Output those which cannot be partitioned.

**-s**- force output to sparse6 format
**-g**- force output to graph6 format If neither
**-s**or**-g**are given, the output format is determined by the header or, if there is none, by the format of the first input graph. Also see**-S**.

- The output file will have a header if and only if the input file does.

**-p**- Read a cubic graph and use its prism. Vertex i of the input becomes

- vertices 2*i,2*i+1 in the prism.

**-x**- Test for decompositions using each 2-path
**-X**- As
**-x**but only output if two 2-paths are missed at some vertex **-y**- Test for decompositions using each non-triangular 3-path

**-t**# With **-x** and **-X**, consider only paths
with center #

- With
**-y**, consider only paths starting at #

**-Y**- With
**-p**, only consider paths whose central edge is vertical **-v**- Give a partition for those graphs who have one and a message for those
which don't. With
**-x**, list exceptional 2-paths.

**-L**# Limit to 1000*# iterations; write with message if
timeout.

- Graphs that time out are written to the output.

**-q**- suppress auxiliary information

March 2021 | nauty 2.7.1 |