gramoloss/lib/tests/chromatic_number.js

Graph theory package for edition and computation

"use strict";
Object.defineProperty(exports, "__esModule", { value: true });
const graph_1 = require("../graph");
// chi(Pn) = 2 
// chi(Cn) = 2 or 3 if n is odd, for n >= 3
// chi(Kn) = n
console.log("chi(P2) = 2");
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2]]).chromaticNumber() == 2);
console.log("chi(P3) = 2");
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 3]]).chromaticNumber() == 2);
console.log("chi(K3) = 3");
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 0]]).chromaticNumber() == 3);
console.log("chi(K4) = 4");
console.log(graph_1.Graph.clique(4).chromaticNumber() == 4);
console.log("chi(K5) = 5");
console.log(graph_1.Graph.clique(5).chromaticNumber() == 5);
console.log("chi(C5) = 3");
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 3], [3, 4], [4, 0]]).chromaticNumber() == 3);
console.log("chi(Petersen) = 3");
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 3], [3, 4], [4, 0], [0, 5], [1, 6], [2, 7], [3, 8], [4, 9], [5, 7], [7, 9], [9, 6], [6, 8], [8, 5]]).chromaticNumber() == 3);
// Speed test
const petersenGraph = graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 3], [3, 4], [4, 0], [0, 5], [1, 6], [2, 7], [3, 8], [4, 9], [5, 7], [7, 9], [9, 6], [6, 8], [8, 5]]);
const lgp = graph_1.Graph.lineGraph(petersenGraph);
console.time('chromaticNumber');
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2]]).chromaticNumber() == 2);
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 3]]).chromaticNumber() == 2);
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 0]]).chromaticNumber() == 3);
console.log(graph_1.Graph.fromEdges([[0, 1], [0, 2], [0, 3], [1, 2], [1, 3], [2, 3]]).chromaticNumber() == 4);
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 3], [3, 4], [4, 0]]).chromaticNumber() == 3);
console.log(graph_1.Graph.fromEdges([[0, 1], [1, 2], [2, 3], [3, 4], [4, 0], [0, 5], [1, 6], [2, 7], [3, 8], [4, 9], [5, 7], [7, 9], [9, 6], [6, 8], [8, 5]]).chromaticNumber() == 3);
console.timeEnd('chromaticNumber');
console.time('vPetersen');
const n = 6;
const g = graph_1.Graph.clique(n);
const lgp2 = graph_1.Graph.lineGraph(g);
const cliques = new Set();
for (let i = 0; i < n; i++) {
    const clique = new Set();
    for (const link of g.links.values()) {
        if (link.startVertex.index == i || link.endVertex.index == i) {
            const vertexLink = lgp2.vertices.get(link.index);
            if (typeof vertexLink != "undefined") {
                clique.add(vertexLink);
            }
        }
    }
    cliques.add(clique);
}
console.log(lgp2.chromaticNumber(cliques));
console.timeEnd('vPetersen');
console.log(petersenGraph.minimalProperColoring());
checkGeomChromaticClique(4);
// K4 in circle should have GCI 4
function checkGeomChromaticClique(n) {
    const g2 = new graph_1.Graph();
    const v0 = g2.addVertex(0, 0, 0);
    const v1 = g2.addVertex(1, 1, 0);
    const v2 = g2.addVertex(2, 0, 1);
    const v3 = g2.addVertex(3, 1, 1);
    g2.addEdge(v0, v1);
    g2.addEdge(v0, v2);
    g2.addEdge(v0, v3);
    g2.addEdge(v1, v2);
    g2.addEdge(v1, v3);
    g2.addEdge(v2, v3);
    const glg2 = graph_1.Graph.geometricLineGraph(g2);
    const cliques = new Set();
    for (let i = 0; i < n; i++) {
        const clique = new Set();
        for (const link of g2.links.values()) {
            if (link.startVertex.index == i || link.endVertex.index == i) {
                const vertexLink = glg2.vertices.get(link.index);
                if (typeof vertexLink != "undefined") {
                    clique.add(vertexLink);
                }
            }
        }
        cliques.add(clique);
    }
    console.log(glg2.chromaticNumber(cliques));
    // console.log(glg2.minimalProperColoring(cliques));
}