Linear embeddings of graphs and graph limits
نویسندگان
چکیده
منابع مشابه
Linear embeddings of graphs and graph limits
Many real-life networks can be modelled by stochastic processes with a spatial embedding. In such processes, the link probability decreases with distance. Using the theory of graph limits, we show how to recognize graph sequences produced by random graph processes with a linear embedding (a natural embedding into R). We define an operator Γ which applies to graph limits, which assumes the value...
متن کاملLabeling Subgraph Embeddings and Cordiality of Graphs
Let $G$ be a graph with vertex set $V(G)$ and edge set $E(G)$, a vertex labeling $f : V(G)rightarrow mathbb{Z}_2$ induces an edge labeling $ f^{+} : E(G)rightarrow mathbb{Z}_2$ defined by $f^{+}(xy) = f(x) + f(y)$, for each edge $ xyin E(G)$. For each $i in mathbb{Z}_2$, let $ v_{f}(i)=|{u in V(G) : f(u) = i}|$ and $e_{f^+}(i)=|{xyin E(G) : f^{+}(xy) = i}|$. A vertex labeling $f$ of a graph $G...
متن کاملUniform Linear Embeddings of Spatial Random Graphs
In a random graph with a spatial embedding, the probability of linking to a particular vertex v decreases with distance, but the rate of decrease may depend on the particular vertex v, and on the direction in which the distance increases. In this article, we consider the question when the embedding can be chosen to be uniform, so the probability of a link between two vertices depends only on th...
متن کاملQuasi-random graphs and graph limits
We use the theory of graph limits to study several quasirandom properties, mainly dealing with various versions of hereditary subgraph counts. The main idea is to transfer the properties of (sequences of) graphs to properties of graphons, and to show that the resulting graphon properties only can be satisfied by constant graphons. These quasi-random properties have been studied before by other ...
متن کاملMonotone Graph Limits and Quasimonotone Graphs
The recent theory of graph limits gives a powerful framework for understanding the properties of suitable (convergent) sequences (Gn) of graphs in terms of a limiting object which may be represented by a symmetric function W on [0, 1], i.e., a kernel or graphon. In this context it is natural to wish to relate specific properties of the sequence to specific properties of the kernel. Here we show...
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: Journal of Combinatorial Theory, Series B
سال: 2015
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2015.02.002