should work

pandas/core/frame.py

@@ -3205,9 +3205,13 @@ def to_html(
             Convert the characters <, >, and & to HTML-safe sequences.
         notebook : {True, False}, default False
             Whether the generated HTML is for IPython Notebook.
-        border : int
-            A ``border=border`` attribute is included in the opening
-            `<table>` tag. Default ``pd.options.display.html.border``.
+        border : int or bool
+            When an integer value is provided, it sets the border attribute in
+            the opening tag, specifying the thickness of the border.
+            If ``False or 0 (zero)`` is passed, the border attribute will not
+            be present in the `<table>` tag.
+            The default value for this parameter is governed by
+            ``pd.options.display.html.border``.
         table_id : str, optional
             A css id is included in the opening `<table>` tag if specified.
         render_links : bool, default False

pandas/io/formats/format.py

@@ -897,9 +897,14 @@ def to_html(
             ``<table>`` tag, in addition to the default "dataframe".
         notebook : {True, False}, optional, default False
             Whether the generated HTML is for IPython Notebook.
-        border : int
-            A ``border=border`` attribute is included in the opening
-            ``<table>`` tag. Default ``pd.options.display.html.border``.
+        border : int or bool
+            When an integer value is provided, it sets the border attribute in
+            the opening tag, specifying the thickness of the border.
+            If ``False or 0 (zero)`` is passed, the border attribute will not
+            be present in the `<table>`tag.
+
+            The default value for this parameter is governed by
+            ``pd.options.display.html.border``.
         table_id : str, optional
             A css id is included in the opening `<table>` tag if specified.
         render_links : bool, default False