Pith Number

pith:BEDPAEP3

pith:2026:BEDPAEP3IIQI4EYPRT3PDV67HE

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Span capacities of graphs

Aljo\v{s}a \v{S}uba\v{s}i\'c, Andrej Taranenko, Christopher Mouron, Mateja Gra\v{s}i\v{c}, Tanja Vojkovi\'c

The d-capacity counts the maximum players who can simultaneously traverse every vertex of a graph while staying at least d apart, reaching the theoretical maximum for d=1 exactly when the graph is topfull.

arxiv:2605.16852 v1 · 2026-05-16 · math.CO

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\usepackage{pith}
\pithnumber{BEDPAEP3IIQI4EYPRT3PDV67HE}

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Record completeness

1 Bitcoin timestamp

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

We characterize topfull graphs, where the 1-capacities reach their theoretical maximum, establishing a connection to graph factorizations and connectivity.

C2weakest assumption

The movement rules under which players traverse the graph are assumed to be defined so that a finite maximum number of simultaneous traversals exists and can be attained for the graph classes studied (paths, cycles, bipartite graphs, and topfull graphs).

C3one line summary

Defines d-capacity for graphs, computes exact values for paths and cycles, gives bounds for bipartite graphs, and characterizes topfull graphs via factorizations and connectivity.

References

12 extracted · 12 resolved · 0 Pith anchors

[1] Baniˇ c and A 2023

[2] T. Dravec, M. Mikalaˇ cki, and A. Taranenko. Graphs with span 1 and shortest optimal walks.Appl. Math. Comput., 500:129433, 2025 2025

[3] G. Erceg, A. ˇSubaˇ si´ c, and T. Vojkovi´ c. Some results on the maximal safety distance in a graph.Filomat, 37(15):5123–5136, 2023 2023

[4] Graˇ siˇ c, C 2026

[5] Lov´ asz and M 2009

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:03:26.257797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0906f011fb42208e130f8cf6f1d7df392f2991ed09f5b2aa0206dd17f63bd23d

Aliases

arxiv: 2605.16852 · arxiv_version: 2605.16852v1 · doi: 10.48550/arxiv.2605.16852 · pith_short_12: BEDPAEP3IIQI · pith_short_16: BEDPAEP3IIQI4EYP · pith_short_8: BEDPAEP3

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BEDPAEP3IIQI4EYPRT3PDV67HE \
  | 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: 0906f011fb42208e130f8cf6f1d7df392f2991ed09f5b2aa0206dd17f63bd23d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9be05aa751fb242be0b7ccdd0e48049299832f242632d4cb53c05954fc79d000",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2026-05-16T07:32:36Z",
    "title_canon_sha256": "9351c362895ad27e24b5b3469c90d9047c445891afeeaf6326ede9e39690b12d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16852",
    "kind": "arxiv",
    "version": 1
  }
}