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THRESHOLD GRAPH LIMITS AND RANDOM THRESHOLD GRAPHS
Limit theory the threshold figure model random threshold figure
2015/7/8
We study the limit theory of large threshold graphs and apply this to a variety of models for random threshold graphs. The results give a nice set of examples for the emerging theory of graph limits.
RANDOM GRAPHS WITH A GIVEN DEGREE SEQUENCE。
A directed graph is set-homogeneous if, whenever U and V are isomorphic finite subdigraphs, there is an automorphism g of the digraph with U^g=V. Here, extending work of Lachlan on finite homogeneous...
Induced subgraphs in sparse random graphs with given degree sequence
Induced subgraphs math
2010/11/22
For any $S\subset [n]$, we compute the probability that the subgraph of $\mathcal{G}_{n,d}$ induced by $S$ is a given graph $H$ on the vertex set $S$. The result holds for any $d=o(n^{1/3})$ and is fu...
The rainbow connectivity of Cayley graphs of Abelian groups
The rainbow connectivity Cayley graphs of Abelian groups
2010/11/9
A path in an edge-colored graph $G$, where adjacent edges may have the same color, is called a rainbow path if no two edges of the path are colored the same. The rainbow connectivity $rc(G)$ of $G$ i...
Segment representation of a subclass of co-planar graphs
Segment representation a subclass of co-planar graphs
2010/11/11
A graph is said to be a segment graph if its vertices can be mapped to line segments in the plane such that two vertices have an edge between them if and only if their corresponding line segments int...
Connectivity and Minimal Distance Spectral Radius of Graphs
Connectivity Spectral Radius of Graphs
2010/11/15
In this paper, we study how the distance spectral radius behaves when the graph is perturbed by grafting edges. As applications, we also determine the graph with $k$ cut vertices (respectively, $k$ cu...
Spectral distributions of adjacency and Laplacian matrices of random graphs
Spectral distributions Laplacian matrices random graphs
2010/11/18
In this paper, we investigate the spectral properties of the adjacency and the Laplacian matrices of random graphs. We prove that: (i) the law of large numbers for the spectral norms and the largest ...
The Fractional Chromatic Number of Triangle-free Graphs with $\Delta\leq 3$
Triangle-free Graphs Combinatorics
2010/11/18
Let $G$ be any triangle-free graph with maximum degree $\Delta\leq 3$. Staton proved that the independence number of $G$ is at least $\frac{5}{14}n$. Heckman and Thomas conjectured that Staton's resul...
A New Class of Antimagic Cartesian Product Graphs.
Antimagic Magic Labeling Regular graph Cartesian product
2012/11/30
An antimagic labeling of a finite undirected simple graph with m edges and n vertices is a bijection from the set of edges to the integers 1; : : : ;m such that all n-vertex sums are pairwise distinct...
Graph-Laplacians and Dirac Operators on (Infinite) Graphs and the Calculation of the Connes-Distance-Functional
Graph-Laplacians Dirac Operators Calculation the Connes-Distance-Functional
2010/11/1
We develop a graph-Hilbert-space framework, inspired by non-commutative geometry, on (infinite) graphs and use it to study spectral properies of \tit{graph-Laplacians} and so-called \tit{graph-Dirac-o...