منابع مشابه
The inducibility of blow-up graphs
The blow-up of a graph is obtained by replacing every vertex with a finite collection of copies so that the copies of two vertices are adjacent if and only if the originals are. If every vertex is replaced with the same number of copies, then the resulting graph is called a balanced blow-up. We show that any graph which contains the maximum number of induced copies of a sufficiently large balan...
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The Blow-up Lemma established by Komlós, Sárközy, and Szemerédi in 1997 is an important tool for the embedding of spanning subgraphs of bounded maximum degree. Here we prove several generalisations of this result concerning the embedding of a-arrangeable graphs, where a graph is called aarrangeable if its vertices can be ordered in such a way that the neighbours to the right of any vertex v hav...
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We develop a combinatorial model to study the evolution of graphs underlying proofs during the process of cut elimination. Proofs are two-dimensional objects and di erences in the behavior of their cut elimination can often be accounted for by di erences in their two-dimensional structure. Our purpose is to determine geometrical conditions on the graphs of proofs to explain the expansion of the...
متن کاملAn approximate blow-up lemma for sparse pseudorandom graphs
We state a sparse approximate version of the blow-up lemma, showing that regular partitions in sufficiently pseudorandom graphs behave almost like complete partite graphs for embedding graphs with maximum degree ∆. We show that (p, γ)-jumbled graphs, with γ = o(pmax(2∆,∆+3/2)n), are “sufficiently pseudorandom”. The approach extends to random graphs Gn,p with p ( log n n )1/∆.
متن کاملThe Inducibility of Graphs on Four Vertices
We consider the problem of determining the maximum induced density of a graph H in any graph on n vertices. The limit of this density as n tends to infinity is called the inducibility of H . The exact value of this quantity is known only for a handful of small graphs and a specific set of complete multipartite graphs. Answering questions of Brown-Sidorenko and Exoo we determine the inducibility...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2014
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2014.06.005