sliver vs carve up

sliver is a noun but carve up is not a noun.

Word	Noun	Adjective	Verb	Adverb
sliver	Yes	No	Yes	No
carve up	No	No	Yes	No

As verbs, carve up is a hypernym of sliver; that is, carve up is a word with a broader meaning than sliver:

Other hypernyms of sliver include dissever, divide, separate, split, split up.

sliver (noun)	carve up (noun)
a thin fragment or slice (especially of wood) that has been shaved from something
a small thin sharp bit of wood or glass or metal

sliver (verb)	carve up (verb)
break up into splinters or slivers	separate into parts or portions
form into slivers
divide into slivers or splinters