private void showCheckedNodesButton_Click(object sender, EventArgs e)
{
    // Disable redrawing of treeView1 to prevent flickering 
    // while changes are made.
    treeView1.BeginUpdate();

    // Collapse all nodes of treeView1.
    treeView1.CollapseAll();

    // Add the checkForCheckedChildren event handler to the BeforeExpand event.
    treeView1.BeforeExpand += checkForCheckedChildren;

    // Expand all nodes of treeView1. Nodes without checked children are 
    // prevented from expanding by the checkForCheckedChildren event handler.
    treeView1.ExpandAll();

    // Remove the checkForCheckedChildren event handler from the BeforeExpand 
    // event so manual node expansion will work correctly.
    treeView1.BeforeExpand -= checkForCheckedChildren;

    // Enable redrawing of treeView1.
    treeView1.EndUpdate();
}

// Prevent expansion of a node that does not have any checked child nodes.
private void CheckForCheckedChildrenHandler(object sender, 
    TreeViewCancelEventArgs e)
{
    if (!HasCheckedChildNodes(e.Node)) e.Cancel = true;
}

// Returns a value indicating whether the specified 
// TreeNode has checked child nodes.
private bool HasCheckedChildNodes(TreeNode node)
{
    if (node.Nodes.Count == 0) return false;
    foreach (TreeNode childNode in node.Nodes)
    {
        if (childNode.Checked) return true;
        // Recursively check the children of the current child node.
        if (HasCheckedChildNodes(childNode)) return true;
    }
    return false;
}