Pith Number

pith:OVY6D66B

pith:2026:OVY6D66BV7RPUHVN4RUPJRFHC7

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A merging procedure for labelings of bipartite graphs

Lucia Marino, Paola Bonacini

A merging procedure produces (A,B)-uniformly ordered labelings for bipartite graphs built by iteratively adding even cycles and pendant paths.

arxiv:2605.13610 v1 · 2026-05-13 · math.CO

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Record completeness

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2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

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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

Through a merging procedure, we are able to get this type of labeling for a specific class of bipartite graphs, which are obtained by iteratively adding an even cycle and a pendant path.

C2weakest assumption

That the merging operation on two (A,B)-uniformly ordered labelings always produces a valid labeling on the combined graph without violating the separation condition or the range requirements.

C3one line summary

A merging procedure produces (A,B)-uniformly ordered labelings for a class of bipartite graphs formed by iteratively adding even cycles and pendant paths, yielding cyclic G-decompositions of K_{2mx+1}.

References

5 extracted · 5 resolved · 0 Pith anchors

[1] K. Brewington, R. C. Bunge, L. J. Cross, S. I. El-Zanati, C. K. Pawlak, J. L. Smith, S. M. Zeppetello,On cyclicG-designs whereGis the one-point union of two cycles, J. Combin. Math. Combin. Comput. 83 2012

[2] R. C. Bunge, S. I. El-Zanati, W. O’Hanlon, C. Vanden Eynden,Onγlabeling the almost bipartite graphP m +e, Ars Combin. 107 (2012), 65–80 2012

[3] S. I. El-Zanati, C. Vanden Eynden, N. Punnim,On the cyclic decomposition of com- plete graphs into bipartite graphs, Australas. J. Combin.24(2001), 209–219 2001

[4] J. A. Gallian,A Dynamic Survey of Graph Labeling, Dynamic Survey 6, Electron. J. Combin., (2025), 805 pp 2025

[5] Rosa,On certain valuations of the vertices of a graph, in:Th´ eorie des graphes, journ´ ees internationales d’´ etudes, Rome 1966 (Dunod, Paris, 1967), 349–355 1966

Receipt and verification

First computed	2026-05-18T02:44:18.069176Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7571e1fbc1afe2fa1eade468f4c4a717c01b27fbb34a352712258ba380fb4901

Aliases

arxiv: 2605.13610 · arxiv_version: 2605.13610v1 · doi: 10.48550/arxiv.2605.13610 · pith_short_12: OVY6D66BV7RP · pith_short_16: OVY6D66BV7RPUHVN · pith_short_8: OVY6D66B

Agent API

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/OVY6D66BV7RPUHVN4RUPJRFHC7 \
  | 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: 7571e1fbc1afe2fa1eade468f4c4a717c01b27fbb34a352712258ba380fb4901

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd9f425bb3798195939070dfde85670092edb7f3728b54a1797586cf2411d1b2",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-13T14:43:31Z",
    "title_canon_sha256": "c37ac3247b6ba830812a16058fa813dd0e67fc1e62e9cb5f293031f6cba2c188"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13610",
    "kind": "arxiv",
    "version": 1
  }
}