Pith Number

pith:HUDCNRHT

pith:2025:HUDCNRHTPSBIVURJ67M6FGIRMQ

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Connectivity-Preserving Important Separators: A Framework for Cut-Uncut Problems

Batya Kenig

Connectivity-preserving important separators can be enumerated in 2^{O(k log k)} time, extending classical separator techniques to cut-uncut problems that require both disconnection and internal connectivity preservation.

arxiv:2511.15849 v4 · 2025-11-19 · cs.DS · cs.CC

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Our main result shows that this family is highly structured: the number of connectivity-preserving important separators of size at most k is 2^{O(k log k)}, and they can be enumerated within the same bound up to polynomial factors.

C2weakest assumption

The framework assumes that the connectivity constraints (equivalence classes of terminals that must remain connected) are provided explicitly and that the underlying graph is undirected and simple; if the constraints are implicit or the graph has directed edges or weights, the enumeration bound may not apply directly.

C3one line summary

Connectivity-preserving important separators of size at most k number 2^{O(k log k)} and can be enumerated in the same bound, yielding 2^{O(k log k)} FPT time for constant-class Node Multiway Cut-Uncut.

Receipt and verification

First computed	2026-07-02T01:18:05.431691Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3d0626c4f37c828ad229f7d9e299116414306ac4d785b76a8359dbc47ce0cc6b

Aliases

arxiv: 2511.15849 · arxiv_version: 2511.15849v4 · doi: 10.48550/arxiv.2511.15849 · pith_short_12: HUDCNRHTPSBI · pith_short_16: HUDCNRHTPSBIVURJ · pith_short_8: HUDCNRHT

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HUDCNRHTPSBIVURJ67M6FGIRMQ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 3d0626c4f37c828ad229f7d9e299116414306ac4d785b76a8359dbc47ce0cc6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e17ab94403a79cb79060ee4bd69dcb261e7b7f149aec50304c0117e2b32c33a6",
    "cross_cats_sorted": [
      "cs.CC"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2025-11-19T20:13:23Z",
    "title_canon_sha256": "8ccdc1d3184d9ab0cd2b4df4350cd9417b4e4183a9121849c9c26fdac2e17bc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2511.15849",
    "kind": "arxiv",
    "version": 4
  }
}