Here is the Texas Statute. It looks like it prevents fixed blade knives with BLADES over 5 1/2 inches. Dagger is also defined--I not certain, but, it appears dagger only applies to longer fixed-blade, slender knives.

(6) "Illegal knife" means a:
(A) knife with a blade over five and one-half inches;
hand instrument designed to cut or stab another by
being thrown;
(C) dagger, including but not limited to a dirk, stiletto,
and poniard;
(D) sword; or
(E) spear.
(7) "Knife" means any bladed hand instrument that is capable
of inflicting serious bodily injury or death by cutting or
stabbing a person with the instrument.
- 46.03. Places weapons prohibited.
(a) A person commits an offense if, with a firearm, illegal
knife, club, or prohibited weapon [includes switchblade
knives], he intentionally, knowingly, or recklessly goes:
(1) on the physical premises of a school [or school bus];
(2) on the premises of a polling place...
[(3) a court; (4) a racetrack; (5) secured area of an
airport].

Edit--Not sure why there is a beer mug in the Statute--it's wasn't there when I posted it!