利用老师教的知识，自己先手动实现一遍

/**
 * graph
 * 0 - 3
 * | \ |
 * 1 - 2
 *
 *
 *  0 - 3
 *   \ |
 * 1 - 2
 * @param {*} graph
 */
function hamiltonCycle(graph, s) {
	let path = [];
	let size = graph.length;
	let visited = Array(size).fill(false);
	let flag = false;
	let count = 0;

	let clonePath = null;

	function print() {
		console.log("-".repeat(count), ...arguments);
	}

	function dfs(v, parent) {
		visited[v] = true;
		path.push(v);
		++count;
		print("push:", v);
		print("push: path=", path);
		print("visited:", visited);

		for (const w of graph[v]) {
			if (flag) {
				break;
			}
			if (!visited[w] && !flag) {
				dfs(w, v);
			} else if (visited[w] && w != parent) {
				if (count === size) {
					flag = true;
					t = w;
					clonePath = path.slice(0);
					print("find solution: ", path);
				}
			}
		}

		visited[v] = false;
		print("pop:", path[path.length - 1]);
		path.pop();
		print("pop: path=", path);
		print("visited:", visited);
		--count;

		print("pop: path=", path);
	}

	dfs(s, s);

	if (!flag) {
		console.log("找不到哈米尔顿回路");
		return [];
	}

	clonePath.push(s);

	return clonePath.reverse();
}

let path = hamiltonCycle(
	[
		[3, 2, 1],
		[0, 2],
		[1, 0, 3],
		[0, 2],
	],
	0,
	0
);
console.log(path.join("->"));

输出结果

- push: 0
- push: path= [ 0 ]
- visited: [ true, false, false, false ]
-- push: 3
-- push: path= [ 0, 3 ]
-- visited: [ true, false, false, true ]
--- push: 2
--- push: path= [ 0, 3, 2 ]
--- visited: [ true, false, true, true ]
---- push: 1
---- push: path= [ 0, 3, 2, 1 ]
---- visited: [ true, true, true, true ]
---- find solution:  [ 0, 3, 2, 1 ]
---- pop: 1
---- pop: path= [ 0, 3, 2 ]
---- visited: [ true, false, true, true ]
--- pop: path= [ 0, 3, 2 ]
--- pop: 2
--- pop: path= [ 0, 3 ]
--- visited: [ true, false, false, true ]
-- pop: path= [ 0, 3 ]
-- pop: 3
-- pop: path= [ 0 ]
-- visited: [ true, false, false, false ]
- pop: path= [ 0 ]
- pop: 0
- pop: path= []
- visited: [ false, false, false, false ]
 pop: path= []
0->1->2->3->0