A yojijukugo describing someone who is extremely stubborn and unyielding, often with a nuance of being firmly set in one's ways. Used as a noun or adjectival noun.
My father is stubborn and never changes his mind once he has decided something.
彼の頑固一徹な態度には手を焼いている。
I'm at my wits' end with his obstinate attitude.
頑固 is the common word for 'stubborn'. 頑固一徹 is a stronger, more emphatic yojijukugo emphasizing unyielding stubbornness.
一徹 alone means 'stubborn' or 'single-minded', but is less common. 頑固一徹 combines both for emphasis.
A yojijukugo combining 頑固 (stubborn) and 一徹 (single-minded, obstinate). The exact historical derivation is uncertain, but it likely arose as an emphatic compound to describe extreme stubbornness.