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The symmetric difference of two graphs G1,G2 on the same set of vertices [n]={1,2,…,n} is the graph on [n] whose set of edges are all edges that belong to exactly one of the two graphs G1,G2. Let H be a fixed graph with an even (positive) number of edges, and let DH(n) denote the maximum possible cardinality of a family of graphs on [n] containing no two members whose symmetric difference is a copy of H. Is it true that [Formula presented] for any such H? We discuss this problem, compute the value of DH(n) up to a constant factor for stars and matchings, and discuss several variants of the problem including ones that have been considered in earlier work.

Original languageEnglish (US)
Article number103880
JournalEuropean Journal of Combinatorics
StatePublished - Feb 2024

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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