相关论文: Testing a Graph-Theoretic Condition for Aggregatin…
The Graph Isomorphism problem has both theoretical and practical interest. In this paper we present an algorithm, called conauto-1.2, that efficiently tests whether two graphs are isomorphic, and finds an isomorphism if they are. This…
We prove some results concerning Alcuin number of graphs. First, we classify graphs which have unique minimum vertex cover. Then we present two necessary conditions for a graph to be of class two and show why one of them (condition on…
The Perfect Graph Theorems are important results in graph theory describing the relationship between clique number $\omega(G) $ and chromatic number $\chi(G) $ of a graph $G$. A graph $G$ is called \emph{perfect} if $\chi(H)=\omega(H)$ for…
A polynomial algorithm for graphs' isomorphism testing is constructed in assumption that there exists a corresponding polynomial algorithm for graphs with trivial automorphism group.
We study the problem of testing for the presence of random effects in mixed models with high-dimensional fixed effects. To this end, we propose a rank-based graph-theoretic approach to test whether a collection of random effects is zero.…
Deep learning-based graph generation approaches have remarkable capacities for graph data modeling, allowing them to solve a wide range of real-world problems. Making these methods able to consider different conditions during the generation…
We automatically verify the crucial steps in the original proof of correctness of an algorithm which, given a geometric graph satisfying certain additional properties removes edges in a systematic way for producing a connected graph in…
In network tomography, one goal is to identify a small set of failed links in a network, by sending a few packets through the network and seeing which reach their destination. This problem can be seen as a variant of combinatorial group…
This work studies fundamental limits for recovering the underlying correspondence among multiple correlated graphs. In the setting of inhomogeneous random graphs, we present and analyze a matching algorithm: first partially match the graphs…
In this paper we present distributed testing algorithms of graph properties in the CONGEST-model [Censor-Hillel et al. 2016]. We present one-sided error testing algorithms in the general graph model. We first describe a general procedure…
This article is concerned with an example of complex planar geometry arising from flat origami challenges. The complexity of solution algorithms is illustrated, depending on the depth of the initial analysis of the problem, starting from…
We study online robust matrix completion on graphs. At each iteration a vector with some entries missing is revealed and our goal is to reconstruct it by identifying the underlying low-dimensional subspace from which the vectors are drawn.…
Existing approaches to solving combinatorial optimization problems on graphs suffer from the need to engineer each problem algorithmically, with practical problems recurring in many instances. The practical side of theoretical computer…
We consider new parameters for conditional network vulnerability related to graph coloring. We define a network to be in operation if the chromatic number (or index) is greater than some specified value k. The parameters of interest, the…
Topological indices are important bridge between graph theory and chemical applications. The study of graph matching expandability has been an influential topic in recent research on graph structure. In this paper, we provide some…
A necessary and sufficient condition is found for a graph $G$, which satisfies the equality $\mu_{21}(G)=|V(G)|$.
It is known that a graph isomorphism testing algorithm is polynomially equivalent to a detecting of a graph non-trivial automorphism algorithm. The polynomiality of the latter algorithm, is obtained by consideration of symmetry properties…
For many types of graphs, criteria have been discovered that give necessary and sufficient conditions for an integer sequence to be the degree sequence of such a graph. These criteria tend to take the form of a set of inequalities, and in…
This paper considers the problem of completing a rating matrix based on sub-sampled matrix entries as well as observed social graphs and hypergraphs. We show that there exists a \emph{sharp threshold} on the sample probability for the task…
The problem of characterizing testable graph properties (properties that can be tested with a number of queries independent of the input size) is a fundamental problem in the area of property testing. While there has been some extensive…