Pair-Trace Absorption Certificates for Regular Induced Subgraphs
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913063989411840 |
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| author | Ramos, Arthur F. Hulak, David Barros de Queiroz, Ruy J. G. B. |
| author_facet | Ramos, Arthur F. Hulak, David Barros de Queiroz, Ruy J. G. B. |
| contents | We study a fixed-core absorption problem for regular induced subgraphs. A set is q-modular if all induced degrees are congruent modulo q. Given a q-modular witness A and a retained core U subset A, we ask when deleting equal-trace q-tuples from A\U can make U into a 2q-modular witness. The main contribution is a finite absorption-or-obstruction certificate. We give an exact quotient formula for the deletion-tail obstruction in complement-orbit coordinates: the correct expression uses oriented differences n_B - n_{U\B}, not sums. Equal-trace q-tuples absorb exactly the span of their trace classes in F_2^U / 1_U. In particular, a connected graph of q-heavy two-point traces on U, together with one odd trace when |U| is even, absorbs every top-bit defect by deleting at most q(|U|-1) tail vertices. If fixed-core absorption fails, the obstruction is an explicit even parity cut of U. We also record the parity base, the terminal modular criterion, and a conditional modular-witness threshold theorem explaining the relevance to the Erdos-Fajtlowicz-Staton problem. The paper does not claim to solve that problem or to improve the general lower bound for F(n). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23882 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pair-Trace Absorption Certificates for Regular Induced Subgraphs Ramos, Arthur F. Hulak, David Barros de Queiroz, Ruy J. G. B. Combinatorics 05C35, 05C55, 05C50 We study a fixed-core absorption problem for regular induced subgraphs. A set is q-modular if all induced degrees are congruent modulo q. Given a q-modular witness A and a retained core U subset A, we ask when deleting equal-trace q-tuples from A\U can make U into a 2q-modular witness. The main contribution is a finite absorption-or-obstruction certificate. We give an exact quotient formula for the deletion-tail obstruction in complement-orbit coordinates: the correct expression uses oriented differences n_B - n_{U\B}, not sums. Equal-trace q-tuples absorb exactly the span of their trace classes in F_2^U / 1_U. In particular, a connected graph of q-heavy two-point traces on U, together with one odd trace when |U| is even, absorbs every top-bit defect by deleting at most q(|U|-1) tail vertices. If fixed-core absorption fails, the obstruction is an explicit even parity cut of U. We also record the parity base, the terminal modular criterion, and a conditional modular-witness threshold theorem explaining the relevance to the Erdos-Fajtlowicz-Staton problem. The paper does not claim to solve that problem or to improve the general lower bound for F(n). |
| title | Pair-Trace Absorption Certificates for Regular Induced Subgraphs |
| topic | Combinatorics 05C35, 05C55, 05C50 |
| url | https://arxiv.org/abs/2604.23882 |