Universal graph - Wikipedia
WEBIn mathematics, a universal graph is an infinite graph that contains every finite (or at-most-countable) graph as an induced subgraph. A universal graph of this type was first constructed by Richard Rado and is now called the Rado graph or random graph.
Universal vertex - Wikipedia
WEBIn graph theory, a universal vertex is a vertex of an undirected graph that is adjacent to all other vertices of the graph. It may also be called a dominating vertex, as it forms a one-element dominating set in the graph.
WEBFour Problems. Problem. Is there a countable universal C-free graph? Is there a countable universal C-free graph with oligomorphic automorphism group? If so, how does one make the graph homogeneous? And is the universal minimal flow metrizable (what is the structural Ramsey theorem)?
WEBOptimal Universal Graphs with Deterministic Embedding. Noga Alon. Michael Capalboy. September 9, 2007. Abstract. Let H be a nite family of graphs. A graph G is H-universal if it contains a copy of each H 2 H as a subgraph. Let H(k; n) denote the family of graphs on n vertices with maximum degree at most ckn2. 2 k.
WEBgraphs for which every two-edge coloring contains a monochromatic H(k;n)-universal graph. In this survey we discuss the main constructions, including some of those that are not optimal, focusing on the methods used, that apply several interesting ideas.
WEBUniversal graphs. Let F be a collection of graphs. Then we say that a graph. U is a universal graph for F if every graph in F is a subgraph of U. Example: = F ; U1 = U2 = Families for universal graphs.
set theory - universal graph - Mathematics Stack Exchange
WEBHint for #1: Suppose that G0 is the purported graph, which contains any graph H unless H in turn contains Kω, the complete countable graph. Make a new graph, G′0, by appending a new vertex v0 to G0 and adding edges from v0 to every vertex of G0.
Universal Graph -- from Wolfram MathWorld
WEBAug 22, 2024 · TOPICS. Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology Alphabetical Index New in MathWorld
WEBAsymptotically optimal induced universal graphs. Noga Alon y. Abstract. We prove that the minimum number of vertices of a graph that contains every graph on k vertices as an induced subgraph is (1 + o(1))2(k 1)=2.
Universal graphs | Guide books - ACM Digital Library
WEBWe introduce and study the problem of constructing geometric graphs that have few vertices and edges and that are universal for planar graphs or for some sub-class of planar graphs; a geometric graph is universal for a class H of planar graphs if ...
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