Like the title said, the adults are zombies and the still living kids make up the main cast.
I remember one specific character who is basically a still-sentient zombie because he’s young. He has a room full of decapitated heads from friendly adults in his past and one of the heads was smiling still or something like that.
I think a later plot point is he gets captured and put in some gladiatorial-esque games hosted by other kids but my memory on that is fuzzy.
Charlie Higson's The Enemy?
Charlie Higson's The Enemy is the first in a jaw-dropping zombie horror series for teens. Everyone over the age of fourteen has succumbed to a deadly zombie virus and now the kids must keep themselves alive.
When the sickness came, every parent, police officer, politician - every adult fell ill. The lucky ones died. The others are crazed, confused and hungry.
Only children under fourteen remain, and they're fighting to survive.
Now there are rumours of a safe place to hide. And so a gang of children begin their quest across London, where all through the city - down alleyways, in deserted houses, underground - the grown-ups lie in wait.
But can they make it there - alive?
Found with search terms of book adult zombies child survivors
I don't see any mention of child zombies, but the main antagonist of the series, St. George, is an intelligent zombie who has at least one case where he carries a decapitated head of one of the kids.
The Wikipedia article for the first book does mention a gladiatorial battle.
Back at the palace, David declares that due to the deaths in the battle, the ownership of the park will be decided in a fight to the death between Achilleus and John. If Achilleus wins, the Palace kids will get control over the park and use it as farmland. If John wins, he will get to keep the park, as well as the freedom to take any resources needed from the palace.
This might be Charlie Higson's The Enemy series, starting with The Enemy (2009). Quoting the blurb of the first book on Goodreads:
When the sickness came, every parent, police officer, politician - every adult fell ill. The lucky ones died. The others are crazed, confused and hungry.
Only children under fourteen remain, and they're fighting to survive.
The adults aren't technically zombies, per SE, but they are cannibalistic revenants:
every grown up 16 years or older sick, crazed, and diseased. Adults overwhelmed with madness tear through the streets of London with a hunger for blood and flesh. Mothers and fathers turn on their own children. Teachers show students whole new kinds of bloody lessons.
(From a review on the same page. Note that the cut-off age apparently changed between editions.)
