Some Universal Graphs
نویسنده
چکیده
It is shown that various classes of graphs have universal elements. In particular, for each n the class of graphs omitting all paths of length n and the class of graphs omitting all circuits of length at least n possess universal elements in all infinite powers.
منابع مشابه
Invariant measures on the set of graphs and homogeneous uncountable universal graphs
We describe the set of all invariant measures on the spaces of universal countable graphs and on the spaces of universal countable triangles-free graphs. The construction uses the description of the S∞-invariant measure on the space of infinite matrices in terms of measurable function of two variables on some special space. In its turn that space is nothing more than the universal continuous (B...
متن کاملInvariant measures and homogeneous uncountable universal graphs
We describe the set of all invariant measures on the spaces of universal countable graphs and on the spaces of universal countable triangles-free graphs. The construction uses the description of the S∞-invariant measure on the space of infinite matrices in terms of measurable function of two variables on some special space. In its turn that space is nothing more than the universal continuous (B...
متن کاملHunting for the New Symmetries in Calabi-Yau Jungles
It was proposed that the Calabi-Yau geometry can be intrinsically connected with some new symmetries, some new algebras. In order to do this it has been analyzed the graphs constructed from K3-fibre CYd (d ≥ 3) reflexive polyhedra. The graphs can be naturally get in the frames of Universal Calabi-Yau algebra (UCYA) and may be decode by universal way with the changing of some restrictions on the...
متن کاملUniversal graphs at the successor of a singular cardinal
The paper is concerned with the existence of a universal graph at the successor of a strong limit singular μ of cofinality א0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such μ there are μ++ graphs on μ+ that taken jointly are universal for the graphs on μ+, while 2μ + >> μ++.
متن کاملExpanders are universal for the class of all spanning trees
Given a class of graphs F , we say that a graph G is universal for F , or F-universal, if every H ∈ F is contained in G as a subgraph. The construction of sparse universal graphs for various families F has received a considerable amount of attention. One is particularly interested in tight F-universal graphs, i. e., graphs whose number of vertices is equal to the largest number of vertices in a...
متن کامل