There are various variants of graph coloring, such as when I want to compute the star chromatic number of a graph, Maple (or Mathematica) seems not to provide relevant functions.
Fortunately, the software ColPack offers this functionality （Note: I just noticed that this software also uses greedy coloring instead of accuracy）. However, it supports the MTX format. So, the question is:
- How can I write a graph in MTX format?
- how can the MTX format be converted into a graph format?
Of course, I would like to perform these operations in Maple. (SageMath may have something)
The following is an example (bcsstk01.mtx） in the directory `ColPack-master/Graphs directory` of the source code of ColPack.
./ColPack -f ../../Graphs/bcsstk01.mtx -m STAR
But I do not know what the graph in the example is. On the contrary, I would like to compute the star chromatic number of the Petersen graph, and I also don't know how to convert it into the MTX format like the above.
I don't understand what the very long decimal numbers (like
2.8322685185200e+06) in the third column in the MTX-file. Will it affect the imformation of the entire graph?
For MTX format, see https://math.nist.gov/MatrixMarket/formats.html. For graphs, the numbers in the third column can all be considered as 1 (with the first two columns representing vertices, and their adjacency). Of course, this is my interpretation and may not necessarily be correct.