Related papers: Recent advances on Dirac-type problems for hypergr…
This MSci thesis surveys results in extremal graph theory, in particular relating to Hamilton cycles. Szem\'eredi's Regularity Lemma plays a central role. We also investigate the robust outexpansion property for digraphs. Kelly showed that…
Discrete versions of the Laplace and Dirac operators haven been studied in the context of combinatorial models of statistical mechanics and quantum field theory. In this paper we introduce several variations of the Laplace and Dirac…
Recent years have witnessed a flurry of research activity in graph matching, which aims at finding the correspondence of nodes across two graphs and lies at the heart of many artificial intelligence applications. However, matching…
Correspondence coloring, or DP-coloring, is a generalization of list coloring introduced recently by Dvo\v{r}\'{a}k and Postle. In this paper we establish a version of Dirac's theorem on the minimum number of edges in critical graphs in the…
Lattice-based cryptography is not only for thwarting future quantum computers, and is also the basis of Fully Homomorphic Encryption. Motivated from the advantage of graph homomorphisms we combine graph homomorphisms with graph total…
Several complications arise in quantum field theory because of the infinite many degrees of freedom. However, the distinction between one-particle and many-particle effects -- mainly induced by the vacuum -- is not clear up to now. A field…
The decision problems of the existence of a Hamiltonian cycle or of a Hamiltonian path in a given graph, and of the existence of a truth assignment satisfying a given Boolean formula $C$, are well-known {\it NP}-complete problems. Here we…
We consider vertex decompositions of (di)graphs which appear in Automata Theory, and establish some their properties. Then we apply them to the problem of forbidden subgraphs.
We associate all small subgraph counting problems with a systematic graph encoding/representation system which makes a coherent use of graphlet structures. The system can serve as a unified foundation for studying and connecting many…
A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger-Feynman-Dyson perturbation expansion and detailed rules are derived for computations. Complexification…
Computers and algorithms play an ever-increasing role in obtaining new results in graph theory. In this survey, we present a broad range of techniques used in computer-assisted graph theory, including the exhaustive generation of all…
Gishboliner, Krivelevich, and Michaeli (2023) conjectured the following generalization of Dirac's theorem: If the minimum degree $\delta$ of an $n$-vertex oriented graph $G$ is greater or equal to $n/2$, then $G$ has a Hamilton oriented…
After the discovery of graphene and its many fascinating properties, there has been a growing interest for the study of "artificial graphenes". These are totally different and novel systems which bear exciting similarities with graphene.…
We propose a universal approach to a range of enumeration problems in graphs. The key point is in contracting suitably chosen symmetric tensors placed at the vertices of a graph along the edges. In particular, this leads to an algorithm…
In graph theory, knowing the number of complete subgraphs with r vertices that a graph g has, limits the number of its complete subgraphs with s vertices, for s > r. A useful upper bound is provided by the Kruskal-Katona theorem, but this…
The aim of this elaborate is presenting the classical symmetric tensors completion problem to an audience of graduate students. As main studying tool, we will introduce the theory of hypergraph rigidity which naturally mirrors the problem…
For an oriented graph $G$, the oriented discrepancy problem concerns the existence of a spanning subgraph of $G$ with a large imbalance between its forward and backward edge orientations. Freschi and Lo proved the Dirac-type Hamilton cycle…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
Dirac algorithm allows to construct Hamiltonian systems for singular systems, and so contributing to its successful quantization. A drawback of this method is that the resulting quantized theory does not have manifest Lorentz invariance.…
We propose a new family of combinatorial inference problems for graphical models. Unlike classical statistical inference where the main interest is point estimation or parameter testing, combinatorial inference aims at testing the global…