Year: 2024
Type: article
Abstract: ABSTRACT A linear graph code is a family of graphs on vertices with the property that the symmetric difference of the edge sets of any two graphs in is also the edge set of a graph in . In this article, we investigate the maximal size of a linear graph code that does not contain a copy of a fixed graph . In particular, we show that if has an even number of edges, the size of the code is , making progress on a question of Alon. Furthermore, we show that for almost all graphs with an even number of edges, there exists such that the size of a linear graph code without a copy of is at most .
Source: Random Structures and Algorithms
DOI: 10.1002/rsa.21263
Author: Leo Versteegen
Institution: University of Cambridge
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,330
OpenAlex ID: W4403469660