C# Recursive delete nodes, C#

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//Rextester.Program.Main is the entry point for your code. Don't change it.
//Compiler version 4.0.30319.17929 for Microsoft (R) .NET Framework 4.5

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text.RegularExpressions;

namespace Rextester
{
    public class Program
    {
        public static void Main(string[] args)
        {
            var d = new Data();
            
            var c0 = d.AddChild(true);
            var c1 = d.AddChild(false);
            
            c0.AddChild(false);
            var c10 = c1.AddChild(false);
            c1.AddChild(false);
            c10.AddChild(true);
            
            Console.WriteLine("Before delete\r\n");
            ShowBranch(d, "1");
            d.DeleteBranchWithNoData();
            Console.WriteLine("\r\nafter delete\r\n");
            ShowBranch(d, "1");
        }
        
       static void ShowBranch(Data node, string location)
       {
           Console.WriteLine("{0} Have Data: {1}", location, node.HaveData);
           for(var i=0; i < node.Children.Count; i++)
           {
               ShowBranch(node.Children[i], location +"."+ (i+1).ToString());
           }
           
       }
    }
    
    public class Data
    {
        
        public Data()
        {
            Children = new List<Data>();
        }
        
        public Data(bool haveData)
            : this()
        {
            HaveData = haveData;
        }
        
        public Data AddChild(bool haveData)
        {
            var child = new Data(haveData);
            Children.Add(child);
            return child;
        }
            
        public List<Data> Children { get; private set; } // c#4, unfortunately... c#6 or above allows for readonly auto-implemented properties.

public bool HaveData { get; set; }
        
        public void DeleteBranchWithNoData()
        {
            var toBeRemoved = new List<Data>();
            foreach(var child in Children)
            {
                if(!child.HaveData && (child.Children == null || !child.Children.Any()))
                {
                    toBeRemoved.Add(child);
                }
                else
                {
                    child.DeleteBranchWithNoData();
                }   
            }
            Children.RemoveAll(d => toBeRemoved.Contains(d));
        }
    }
}

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Compilation time: 0,16 sec, absolute running time: 0,09 sec, cpu time: 0,09 sec, average memory usage: 14 Mb, average nr of threads: 2