Polynomial Reconstruction Problem for Hypergraphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916171689754624 |
|---|---|
| author | Cooper, Joshua Okur, Utku |
| author_facet | Cooper, Joshua Okur, Utku |
| contents | We show that, in general, the characteristic polynomial of a hypergraph is not determined by its ``polynomial deck'', the multiset of characteristic polynomials of its vertex-deleted subgraphs, thus settling the ``polynomial reconstruction problem'' for hypergraphs in the negative. The proof proceeds by showing that a construction due to Kocay of an infinite family of pairs of $3$-uniform hypergraphs which are non-isomorphic but share the same hypergraph deck, in fact, have different characteristic polynomials. The question remain unresolved for ordinary graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_16152 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Polynomial Reconstruction Problem for Hypergraphs Cooper, Joshua Okur, Utku Combinatorics 05C60 (Primary) 05C31, 05C50, 05C65 (Secondary) G.2.2 We show that, in general, the characteristic polynomial of a hypergraph is not determined by its ``polynomial deck'', the multiset of characteristic polynomials of its vertex-deleted subgraphs, thus settling the ``polynomial reconstruction problem'' for hypergraphs in the negative. The proof proceeds by showing that a construction due to Kocay of an infinite family of pairs of $3$-uniform hypergraphs which are non-isomorphic but share the same hypergraph deck, in fact, have different characteristic polynomials. The question remain unresolved for ordinary graphs. |
| title | Polynomial Reconstruction Problem for Hypergraphs |
| topic | Combinatorics 05C60 (Primary) 05C31, 05C50, 05C65 (Secondary) G.2.2 |
| url | https://arxiv.org/abs/2312.16152 |