Ramsey Graphs Induce Subgraphs of Quadratically Many Sizes
نویسندگان
چکیده
منابع مشابه
Ramsey Graphs Induce Subgraphs of Many Different Sizes
A graph on n vertices is said to be C-Ramsey if every clique or independent set of the graph has size at most C log n. The only known constructions of Ramsey graphs are probabilistic in nature, and it is generally believed that such graphs possess many of the same properties as dense random graphs. Here, we demonstrate one such property: for any fixed C > 0, every C-Ramsey graph on n vertices i...
متن کاملSizes of Induced Subgraphs of Ramsey Graphs
An n-vertex graph G is c-Ramsey if it contains neither a complete nor an empty induced subgraph of size greater than c log n. Erdős, Faudree and Sós conjectured that every c-Ramsey graph with n vertices contains Ω(n5/2) induced subgraphs any two of which differ either in the number of vertices or in the number of edges, i.e. the number of distinct pairs (|V (H)|, |E(H)|), as H ranges over all i...
متن کاملRamsey graphs contain many distinct induced subgraphs
It is shown that any graph on n vertices containing no clique and no independent set on t + 1 vertices has at least 2./( 2r2o ~2t)) distinct induced subgraphs.
متن کاملInduced subgraphs of Ramsey graphs with many distinct degrees
An induced subgraph is called homogeneous if it is either a clique or an independent set. Let hom(G) denote the size of the largest homogeneous subgraph of a graph G. In this short paper we study properties of graphs on n vertices with hom(G) ≤ C log n for some constant C. We show that every such graph contains an induced subgraph of order αn in which β √ n vertices have different degrees, wher...
متن کاملRamsey Properties of Random Subgraphs of Pseudo-Random Graphs
Let G = (V,E) be a d-regular graph of order n. Let Gp be the random subgraph of G for which each edge is selected from E(G) independently at random with probability p. For a fixed graph H, define m(H) := max{e(H ′)/(v(H ′)− 1) : H ′ ⊆ H}. We prove that n(m(H)−1)/m(H)/d is a threshold function for Gp to satisfy Ramsey, induced Ramsey, and canonical Ramsey properties with respect to vertex colori...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2018
ISSN: 1073-7928,1687-0247
DOI: 10.1093/imrn/rny064