[JOSS-Review] Code Implementation about graphcoloring HOT 2 OPEN

@ProbShin @jedbrown

• I have added a verbose option to both Backtracking.java and GraphColoring.java (heuristic). But I think some basic information, like what coloring was found should be still outputted.

• The KNOWN_K is actually a lower bound. If known, the backtracking algorithm will spend time on coloring the graph with this chromatic number. It is initialized to the clique size which is a lower bound on the chromatic number of the graph. The algorithm iteratively increments this number and tries to color the graph with this incremented number of colors.

• I have removed the adjacency matrix from the graph. This was only used by the clique algorithm and was not absolutely essential to computing the clique.

Let me know your thoughts. Thank you!

from graphcoloring.

Great.

• Yes, you are right. the number of colors and the color of the vertex are both the output of the algorithm. Since the vertex colors have been stored in the class Graph :: class Node, the number of colors could be output in an integer variable. Print the relative information to the screen can be considered as a debug operation by the users or the developers since this function is independent of the algorithms.

• I see. KNOWN_K is the lower bound. Thanks leading me out. And the clique size is a lower bound of the chromatic number. But unfortunately, there is not an efficient way to get this number out in constant or linear time for general graphs.

• Good, that's also my observation, it seems that the adjacency matrix is not used within the function of colorings.

In all, I am fine with all the modifications. Thanks.

from graphcoloring.