Related papers: Kernels, Truth and Satisfaction
The concept of coreflexive set is introduced to study the structure of digraphs. New characterizations of line digraphs and nth-order line digraphs are given. Coreflexive sets also lead to another natural way of forming an intersection…
Mining for trees in a graph is shown to be NP-complete.
A nut graph is a simple graph of order 2 or more for which the adjacency matrix has a single zero eigenvalue such that all non-zero kernel eigenvectors have no zero entry (i.e. are full). It is shown by construction that every finite group…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Cameron and Kazanidis have recently shown that rank-3 graphs are either cores or have complete cores, and they asked whether this holds for all strongly regular graphs. We prove that this is true for the point graphs and line graphs of…
Let $G$ be a simple, connected and finite graph with order $n$. Denote the independence number, edge independence number and total independence number by $\alpha(G), \alpha'(G)$ and $\alpha"(G)$ respectively. This paper establishes a…
The ability to control a complex network towards a desired behavior relies on our understanding of the complex nature of these social and technological networks. The existence of numerous control schemes in a network promotes us to wonder:…
For a graph $G$ and integer $k\geq1$, we define the token graph $F_k(G)$ to be the graph with vertex set all $k$-subsets of $V(G)$, where two vertices are adjacent in $F_k(G)$ whenever their symmetric difference is a pair of adjacent…
In this paper, we try to determine exact or bounds on the choosability, or list chromatic numbers of some Cayley graphs, typically some Unitary Cayley graphs and Cayley graphs on Dihedral groups.
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.
Most state-of-the-art graph kernels only take local graph properties into account, i.e., the kernel is computed with regard to properties of the neighborhood of vertices or other small substructures. On the other hand, kernels that do take…
A relational structure is a core, if all its endomorphisms are embeddings. This notion is important for computational complexity classification of constraint satisfaction problems. It is a fundamental fact that every finite structure has a…
We enumerate graph homomorphisms to quasi-complete graphs, i.e., graphs obtained from complete graphs by removing one edge. The source graphs are complete graphs, quasi-complete graphs, cycles, paths, wheels and broken wheels. These…
The problem of modifying a given graph to satisfy certain properties has been one of the central topics in parameterized tractability study. In this paper, we study the cycle contraction problem, which makes a graph into a cycle by edge…
Incompleteness theorems of Godel, Turing, Chaitin, and Algorithmic Information Theory have profound epistemological implications. Incompleteness limits our ability to ever understand every observable phenomenon in the universe.…
Large knowledge graphs combine human knowledge garnered from projects ranging from academia and institutions to enterprises and crowdsourcing. Within such graphs, each relationship between two nodes represents a basic fact involving these…
Graph pattern mining methods can extract informative and useful patterns from large-scale graphs and capture underlying principles through the overwhelmed information. Contrast analysis serves as a keystone in various fields and has…
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…
The Knowledge graph (KG) uses the triples to describe the facts in the real world. It has been widely used in intelligent analysis and applications. However, possible noises and conflicts are inevitably introduced in the process of…
In this paper we present a novel graph kernel framework inspired the by the Weisfeiler-Lehman (WL) isomorphism tests. Any WL test comprises a relabelling phase of the nodes based on test-specific information extracted from the graph, for…