Optimal Adjacency Labels for Subgraphs of Cartesian Products
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2022
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913497427738624 |
|---|---|
| author | Esperet, Louis Harms, Nathaniel Zamaraev, Viktor |
| author_facet | Esperet, Louis Harms, Nathaniel Zamaraev, Viktor |
| contents | For any hereditary graph class $F$, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $F$. As a consequence, we show that, if $F$ admits efficient adjacency labels (or, equivalently, small induced-universal graphs) meeting the information-theoretic minimum, then the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $F$ do too. Our proof uses ideas from randomized communication complexity, hashing, and additive combinatorics, and improves upon recent results of Chepoi, Labourel, and Ratel [Journal of Graph Theory, 2020]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02872 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Optimal Adjacency Labels for Subgraphs of Cartesian Products Esperet, Louis Harms, Nathaniel Zamaraev, Viktor Data Structures and Algorithms Combinatorics 05C78, 05C76, 68R10 For any hereditary graph class $F$, we construct optimal adjacency labeling schemes for the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $F$. As a consequence, we show that, if $F$ admits efficient adjacency labels (or, equivalently, small induced-universal graphs) meeting the information-theoretic minimum, then the classes of subgraphs and induced subgraphs of Cartesian products of graphs in $F$ do too. Our proof uses ideas from randomized communication complexity, hashing, and additive combinatorics, and improves upon recent results of Chepoi, Labourel, and Ratel [Journal of Graph Theory, 2020]. |
| title | Optimal Adjacency Labels for Subgraphs of Cartesian Products |
| topic | Data Structures and Algorithms Combinatorics 05C78, 05C76, 68R10 |
| url | https://arxiv.org/abs/2206.02872 |