Four coloring of a graph, for Javascript

Given a map represented as an array of arrays, provide color indices for the cells such that no two adjacent cells have the same color.

That is, "color the map." With a continuous 2d map, this is always possible with no more than four colors.

Given a blank map

You can represent a map as an "adjacency matrix" (here's an adjacency matrix for US states for javascript,)

const states = ["AK", "AL", "AR", ...];

const state_adjacency = [
  [],
  [25, 42, 10, 09],
  [24, 42, 25, 18, 43, 36],
  ...
];

This says "state 0 is Alaska, which has no neighbors; state 1 is Alabama, which has neighbors 25 (Missouri,) 42 (Tennessee,) 10 (Georgia,) and 9 (Florida;) state 2 is Arkansas..."

If you have such a matrix, feed it to this library:

> gen4col(state_adjacency, true);  // true means "only give me one solution;" otherwise you'll get a bunch
[0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 2, 2, 1, 1, 0, 1, 2, 3, 3, 2, 0, 0, 2, 2, 1, 3, 3, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1, 2, 3, 0, 1, 3, 0, 3]

This says "Paint Alaska in color 0, Alabama in 0, Arkansas in 0, Arizona in 0, California in 1, Colorado in 1," and so forth. This allows you to produce a different map:

There is only one method: gen4col(vertexArray, returnOnlyOne).

vertexArray is an array of arrays, where the master offset is the vertex ID, and the items in the subordinate arrays are the connected vertices. All links should be listed bidirectionally.

returnOnlyOne is a boolean which tells the algorithm whether to return only the first solution it finds, or every solution.