Tree Contains LinkedList

Check if a tree with the following structure contains a linked list:

Given the following tree:

- AA

    - B2

        - S1

- B1

And the following linked list:

AA –> B2 –> S1

Test:

    [TestMethod]
        public void TestTreeContainsLInkedlist()
        {
            var tree = new Node("");
            var aaNode = new Node("AA");
            var b2Node = new Node("B2");
            b2Node.Add(new Node("S1"));
            aaNode.Add(b2Node);
            tree.Add(aaNode);
            tree.Add(new Node("B1"));
            var lInkedItem = new LinkedItem("AA", new LinkedItem("B2", new LinkedItem("S1", null)));
            bool contains = TreeContainsLinkedList.Contains(tree, lInkedItem);
            Assert.IsTrue(contains);

            var tree1 = new Node("");
            tree1.Add(new Node("KK"));
            bool doesntContain = TreeContainsLinkedList.Contains(tree1, lInkedItem);
            Assert.IsFalse(doesntContain);
        }
    

Solution:

    public class TreeContainsLinkedList
    {
        public static bool Contains(Node tree, LinkedItem linkedItem)
        {
            LinkedItem currentLinkedItem = linkedItem;
            Node currentNode = tree;
            while (currentLinkedItem != null)
            {
                bool exist = false;
                foreach (Node node1 in currentNode)
                {
                    if (node1.Name == currentLinkedItem.Name)
                    {
                        exist = true;
                        currentNode = node1;
                        break;
                    }
                }
                if (!exist)
                {
                    return false;
                }
                currentLinkedItem = currentLinkedItem.Link;
            }

            return true;
        }
    }

    public class Node : List<Node>
    {
        private readonly string name;

        public Node(string name)
        {
            this.name = name;
        }

        public string Name
        {
            get { return name; }
        }
    }

    public class LinkedItem
    {
        private readonly string name;
        private readonly LinkedItem link;

        public LinkedItem(string name, LinkedItem link)
        {
            this.name = name;
            this.link = link;
        }

        public string Name
        {
            get { return name; }
        }

        public LinkedItem Link
        {
            get { return link; }
        }
    }