Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-07-09T19:58:17.125188Z
Paper Citation Record · LEDGER
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality
As of 15 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 2 inbound Pith citation observations for arXiv:2607.07118.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-14T15:33:15.240468Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-10T07:16:52.886073Z
Reference resolution
22 of 22 outbound references displayed
- verified exact4
- verified fuzzy8
- unresolved10
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation bb64839f-1647-427a-8ef8-3321f06eb79f · outbound
This paper cites Berndsen, Three problems in algebraic combinatorics, Master’s thesis, Eindhoven University of Technology, 2012.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Berndsen, Three problems in algebraic combinatorics, Master’s thesis, Eindhoven University of Technology, 2012
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.925400Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation f728aea1-da80-46ff-9b7b-28891d3f381d · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.927163Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 974153d3-eacb-4a2f-8a30-9b58d68907e7 · outbound
This paper cites More on the full Brouwer Laplacian spectrum conjecture.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality More on the full Brouwer Laplacian spectrum conjecture
Reference 3
- Resolution
- verified exact
- local_arxiv, observed 2026-07-09T20:16:29.587399Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation eb558293-7311-4b56-85c0-626b052a71f6 · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.919597Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 870bd2b4-5070-4d3b-bb03-52e11833c76b · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.921456Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation fa0793ff-ae76-45da-92c6-0238385f6ea9 · outbound
This paper cites Edmonds, Paths, trees, and flowers,Canadian Journal of Mathematics, 17 (1965) 449–467.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Edmonds, Paths, trees, and flowers,Canadian Journal of Mathematics, 17 (1965) 449–467
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.923402Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 3b95e489-8305-4e64-85f9-14f19d0809a5 · outbound
This paper cites Erdős and T.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Erdős and T
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.928889Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation c5f535c4-30fb-457f-a1d2-1fb6ecf29db4 · outbound
This paper cites Fan, On a theorem of Weyl concerning eigenvalues of linear transformations:I,Proceedings of the National Academy of Sciences of the United States of America, 35 (1949) 652–655.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Fan, On a theorem of Weyl concerning eigenvalues of linear transformations:I,Proceedings of the National Academy of Sciences of the United States of America, 35 (1949) 652–655
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.900281Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation d50c7bde-876e-4043-83db-b9e600b42f54 · outbound
This paper cites Fritscher, C.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Fritscher, C
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.912590Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 595febd3-4930-42a2-8011-1299ef2c5ccb · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 10
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.927007Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 5857f6e7-d516-4d7f-bdc8-9e674ca3e1ac · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 11
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.929062Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1f88464f-42ed-457c-a1fe-047a13e8ee98 · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 12
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.930917Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4dac8b9a-bbce-4248-9189-16ff2ae12b08 · outbound
This paper cites On Brouwer's Laplacian conjecture.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality On Brouwer's Laplacian conjecture
Reference 13
- Resolution
- verified exact
- local_arxiv, observed 2026-07-09T20:16:29.586034Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b861a589-304c-4685-9031-5abc3b8e1269 · outbound
This paper cites Lew, An approximate version of Brouwer’s Laplacian conjecture, arXiv:2601.17575, 2026.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Lew, An approximate version of Brouwer’s Laplacian conjecture, arXiv:2601.17575, 2026
Reference 14
- Resolution
- verified exact
- arxiv_id, observed 2026-07-09T20:16:29.582554Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 4fcfdefe-d2ef-4f70-8da3-055ede084b2b · outbound
This paper cites Lew, Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs, Journal of Combinatorial Theory, Series B, 179 (2026) 71–89.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Lew, Partition density, star arboricity, and sums of Laplacian eigenvalues of graphs, Journal of Combinatorial Theory, Series B, 179 (2026) 71–89
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.913395Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation b5b7439f-220a-43d7-b2d8-3eab6160f97a · outbound
This paper cites Sums of Laplacian eigenvalues and sums of degrees.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Sums of Laplacian eigenvalues and sums of degrees
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-07-09T20:16:29.585047Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 477c1e0a-f183-4dee-8760-dfc3c5f5c6ae · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 17
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.932620Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 0abaac29-1062-4052-971e-623160c44814 · outbound
This paper cites Lovasz and M.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Lovasz and M
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.932795Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation ccdfe454-4676-4978-8dea-39e3b42724e9 · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 19
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.930477Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation af8e0ae1-a397-412a-8d85-659049dd3acc · outbound
This paper cites Rocha, Brouwer’s conjecture holds asymptotically almost surely,Linear Algebra and its Applications, 597 (2020) 198–205.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Rocha, Brouwer’s conjecture holds asymptotically almost surely,Linear Algebra and its Applications, 597 (2020) 198–205
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-07-09T20:36:31.905991Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 1a7c89dd-9637-4701-b2c9-a1a0969d3df5 · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.914789Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation a45b830e-53e5-44f1-af36-5b822db2bac9 · outbound
This paper cites an unresolved cited work.
A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-07-09T20:36:31.920964Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Pith citing papers
Observation cb4c328a-21d4-4f57-b388-b59392ecd09b · inbound
Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture cites this paper.
Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality
Reference 12
- Resolution
- verified exact
- local_arxiv, observed 2026-07-10T07:16:52.887822Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.
Observation 96c6b01a-2ea7-4d62-bda0-651659400647 · inbound
Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture cites this paper.
Proofs of two conjectures on generalizations of Brouwer's Laplacian conjecture A Matching-Number Refinement of Brouwer's Laplacian Eigenvalue Inequality
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-07-14T15:33:15.240468Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.