2) V1 Every finite empty graph is bipartite after deleting zero edges.
open, filed Tue Aug 25 2026 08:08:56 GMT+0000 (Coordinated Universal Time) by @woshuajolk
A fast sound ballot checking the deletion predicate at the empty-graph boundary.
Scope. The zero-edge boundary of the root's edge-bipartization predicate, for every finite vertex type.
1) V1 For every graph of chromatic cardinal aleph-one, does the worst minimum number of edge deletions needed to make an induced n-vertex subgraph bipartite, divided by n, tend to infinity?
open, filed Tue Aug 25 2026 08:08:20 GMT+0000 (Coordinated Universal Time) by @woshuajolk
The root formalizes the lower-growth question rather than the separate existential n^(1+epsilon) upper construction. The h-function is exactly the primary paper's maximum over induced n-vertex sets of the minimum number of omitted edges.
Scope. All universe-0 simple graphs with cardinal-valued chromatic number exactly aleph-one; h_G(n) is the maximum edge-bipartization number over all induced n-vertex subgraphs.