Must a married [or once married] woman cover all of the hair of her head?
It is forbidden for a married woman to reveal even a single hair of her head to the public, and hence all of the hair, must be covered. It is for this reason that many of today’s Poskim rule one is to wear a wig [Sheital] rather than a head Kerchief [Tichel], as the wig guarantees the covering of all the hair, as opposed to a head kerchief. Although some Poskim of today novelized that a woman may Bedieved be lenient to uncover up to two finger-worth’s [4 cm] of the top part of her hair, the Rebbe, as well as the vast majority of today’s Poskim, severely negate this opinion, and state it has no place in Shulchan Aruch, and so is the final ruling. Those women who uncover even more than 4 cm of their hair are to be protested according to all.
 Tzemach Tzedek Even Haezer 139/2 from the fact he prohibits the sideburns; Chasam Sofer 36; Ashel Avraham Butchach “Proper to beware against even one hair”; Dovev Meisharim 1/124; Teshuvos Vehanhagos 1/62; Lehoros Nasan 5; Piskeiy Teshuvos 75/10; Chazon Ish in Dinim Vehanhagos 2/88-9; Rebbe Ben Tziyon Aba Shaul brought in Kuntrus Kisui Rosh Leisha; Rav Mashash in Tevuos Shemesh 137; Shemesh Umagen 2/15-17; Az Nidbaru 12/41 that one should cover every hair; Rav Moshe Shternbuch in Daas Vehalacha 1; Rav Lefkovich in Kovetz Beis Hillel 9; Or Yitzchak 3; Nitei Gavriel in Kovetz Or Yisrael 36-37
 Poskim ibid including: Chazon Ish ibid; Rebbe Ben Tziyon Aba Shaul ibid; Or Yitzchak 3 in name of Rav Moshe Feinstein; Letters of Rebbe printed in Shulchan Menachem 6/80-84
 Igros Moshe 4/112; Even Haezer 1/58; However see there that this is only Bedieved; Likewise see Or Yitzchak 3 in name of Rav Moshe Feinstein that even he agreed that initially one should wear a wig in order to cover every hair; Rav Ovdia Yosef in Yalkut Yosef Otzer Dinim allows Bedieved
The reason: As only a Tefach is considered an Erva by a woman [Igros Moshe ibid]; and less than a Tefach is only Rabbincial, and hence less than majority of a Tefach is alwolowed. [Rav Ovadia ibid]
 Igros Kodesh 9/325 [printed in Shulchan Menachem 6/81] “You want to wear a Sheital that will leave two finger-worth’s uncovered! Who are you trying to fool, not the world, but only yourself, and what is the purpose of fooling yourself? The rule is clear in Shulchan Aruch [that all the hair must be covered] and there is no room for question on this matter.” See also Igros Kodesh 16/330 and other letters printed in Shulchan Menachem 6/80-84
 All Poskim brought in previous footnotes