Vuetify v-treeview doesn't delete node - vue.js

Question

I am a beginner in vuejs and vuetify and I try to add and remove nodes in a treeview.
When I do a .push(item) the treeview updates but when I delete an item from my array, the treeview does not update.
Here is an example of my code
My treeview
<v-treeview
[...]
:items="formatedItems"
item-key="slug"
[...]
>
[...]
</v-treeview>
formatedItems is declared in the data like this :
data: () => ({
[...]
formatedItems: [{
id: 0,
slug: null,
name: i18n.t(****),
children: []
}]
[...]
}),
This code correctly adds a child in my treeview :
this.formatedItems[0].children.push({
id: element.id,
slug: element.slug,
name: element.name,
children: []
});
On the other hand, this code removes the item from my array but doesn't update the treeviews :
_.remove(this.formatedItems[0].children, function(n) {
return n.slug == element.slug;
});
this.formatedItems = this.formatedItems; // I tried this to trigger a potential magical update of vuejs but nothing...
I don't know what to try anymore, that's why I come to ask you the question:
.push being a build-in function and knowing that I use a lodash function for deletion, is there something I didn't understand about the use of vuejs that causes my treeview not to be updated?
Thank you for your attention

Answer 1

Looks like the problem somewhere else. I've tried a basic example and all works fine.
Except I used filter method for deletion.
codepen.io/DavidGolodetsky/pen/eYZMbgm