Defect Flow, Incidence Rank, and Boundary Descent for Seymour's Second-Neighborhood Conjecture

We develop a degree-independent structural toolkit for Seymour's second-neighborhood conjecture. The main contributions are block and trap defect factorizations, arbitrary-baseline total-defect balance, protected-parent and Hall-deficiency separator geometry, Boolean defect flow and incidence-rank decomposition, minimum-degree-free host compression, tight-root shell and portal descent, per-arc curvature with repeated-two-path localization, and exact affine certificate interfaces. Known external-boundary descent, triangular finite-witness, and dense-boundary results are used as calibrated prior inputs. The paper does not prove Seymour's conjecture or the minimum-out-degree-eight case. Its exact unresolved endpoint is bounded-capacity routing of repeated-two-path overlap. This record contains version 1.0.0 of the paper, source, bibliography, selected reusable proof records, licenses, deterministic archive manifest, replay script, and checksums.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-23
DOI
https://doi.org/10.5281/zenodo.22068837
Citations
2
Primary Topic
Complexity and Algorithms in Graphs
Type
article
Field-Weighted Citation Impact
12.34
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article

Defect Flow, Incidence Rank, and Boundary Descent for Seymour's Second-Neighborhood Conjecture

Hainan Zhao
2 citations
Zenodo (CERN European Organization for Nuclear Research)
Complexity and Algorithms in Graphs
12.34
article

Defect Flow, Incidence Rank, and Boundary Descent for Seymour's Second-Neighborhood Conjecture

Hainan Zhao
article en
2 citations

Abstract

We develop a degree-independent structural toolkit for Seymour's second-neighborhood conjecture. The main contributions are block and trap defect factorizations, arbitrary-baseline total-defect balance, protected-parent and Hall-deficiency separator geometry, Boolean defect flow and incidence-rank decomposition, minimum-degree-free host compression, tight-root shell and portal descent, per-arc curvature with repeated-two-path localization, and exact affine certificate interfaces. Known external-boundary descent, triangular finite-witness, and dense-boundary results are used as calibrated prior inputs. The paper does not prove Seymour's conjecture or the minimum-out-degree-eight case. Its exact unresolved endpoint is bounded-capacity routing of repeated-two-path overlap. This record contains version 1.0.0 of the paper, source, bibliography, selected reusable proof records, licenses, deterministic archive manifest, replay script, and checksums.

Zenodo (CERN European Organization for Nuclear Research)
Sustainable cities and communities
Openalex Percentile: Top 1%
Complexity and Algorithms in Graphs
12.34
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