When Helen and her son Arpad emigrated in 1906, they both listed their birthplaces as Gyula (which was their last residence, as well.) At the time of emigration, Arpad is 4 years old, so he was born in 1902, approximately.
His birth record should appear in the Civil Records of Gyula, Bekes, Hungary, which have been microfilmed and can be rented at your local Family History Center. This birth record should list his parents' names and their places of birth. You can then theoretically track each parent backward.
Here is a link:https://www.familysearch.org/search/search/library_catalog#s...