this library provides support to construct graphs and their coloring graphs. a coloring graph is a metagraph representing all the valid colorings of a graph. each vertex of a coloring graph represents a coloring of the base graph.

## coloring-graphs

a coloring graphs library written in C++ for speedy computation and wrapped in Python for ease of development and extension!

### what

this library provides support to construct graphs, their coloring graphs, and biconnected component metagraphs. a coloring graph is a graph representing all the valid colorings of a graph. each vertex of a coloring graph represents a coloring of the base graph. two colorings are considered adjacent if they differ in only one vertex's color.

in this project, we represent a coloring as an integer, which, when converted to base k (for a k-coloring), is a number of length |V| and represents the vertex-wise colors [0,k) for each vertex.

the library is under development, being written using Python and C/C++. the web application uses the library to provide useful GUI for quick drawing and graph construction. in the future, we plan to develop a supplemental subsection of the library containing useful graph algorithms and ability to run simulations to test structural graph theoretic conjectures about graph coloring and coloring graphs. for documentation, feel free to take a look inside libcolgraph/ and read the docstrings. for questions, reach out.

### screenshot of the web GUI

[Clockwise] A 7 vertex BaseGraph that is a hexagon with a central vertex and a missing 'spoke' leads to a quite complex ColoringGraph with k=4 colors. You can see the formation of polyps at the edges. The structure of the resultant ColoringGraph is shown in the Meta ColoringGraph produced by a run of modified Tarjan's algorithm for biconnected components. The central 'mothership' can be seen, adjacent to which there are cut vertices, and finally the stray singular coloring vertices at the tips of polyps.

### usage

• as a module

plot a BaseGraph, its ColoringGraph, and the Meta ColoringGraph generated by Tarjans. you would need to have a graph formatted in an adjacency matrix file. opens plots in new browser windows.

basic usage:

colgraphplot [PATH_TO_FILE] [-k COLORS]
---
options:
usage: colgraphplot [-h] [-k COLORS] [-v] [--no-bg] [--no-cg] [--no-mbg]
[--no-mcg]
INPUT_GRAPH

positional arguments:

optional arguments:
-h, --help            show this help message and exit
-k COLORS, --colors COLORS
number of colors to use to create ColoringGraph
-v, --verbosity       set output verbosity
--no-bg               hide BaseGraph?
--no-cg               hide ColoringGraph?
--no-mbg              hide meta BaseGraph?
--no-mcg              hide meta ColoringGraph?

launch web GUI [WIP]:

colgraphweb [OPTIONS]

currently under development.

• as a library

import libcolgraph

bg = libcolgraph.BaseGraph()

cg = bg.build_coloring_graph(4)

print('bg {} led to a cg {}'.format(bg, cg))

for v in cg.get_vertices():
# do something
pass

### installation

• for installation from source refer to detailed install instructions

• pypi

python3 -m pip install libcolgraph [--user] [--upgrade]

things to note:

• currently a binary wheel is available only for manylinux distributions e.g. centOS, Debian family, RedHat family, etc.
• if your distribution is not manylinux-supported, then pip will need to compile locally using swig and setuptools. in that case, make sure you have setuptools and swig installed, as they will be needed for compilation.
• in the future we will release wheels for MacOS as well. these might not be as frequently maintained, however, so your best bet would be to compile locally using swig.

### help

full documentation coming soon

### who

Coloring Graphs lab, University of Richmond. Multiple contributors. (C) 2017-2019