相关论文: Enumerating the Classes of Local Equivalency in Gr…
We systematically study a natural problem in extremal graph theory, to minimize the number of edges in a graph with a fixed number of vertices, subject to a certain local condition: each vertex must be in a copy of a fixed graph $H$. We…
We propose a new step-wise approach to proving observational equivalence, and in particular reasoning about fragility of observational equivalence. Our approach is based on what we call local reasoning. The local reasoning exploits the…
We refine and advance the study of the local structure of idempotent finite algebras started in [A.Bulatov, The Graph of a Relational Structure and Constraint Satisfaction Problems, LICS, 2004]. We introduce a graph-like structure on an…
We establish the connection between a recent new construction technique for quantum error correcting codes, based on graphs, and the so-called stabilizer codes: Each stabilizer code can be realized as a graph code and vice versa.
A colouring of a graph G is called distinguishing if its stabiliser in Aut G is trivial. It has been conjectured that, if every automorphism of a locally finite graph moves infinitely many vertices, then there is a distinguishing…
In the study of deterministic distributed algorithms it is commonly assumed that each node has a unique $O(\log n)$-bit identifier. We prove that for a general class of graph problems, local algorithms (constant-time distributed algorithms)…
We present a new approach to graph limit theory which unifies and generalizes the two most well developed directions, namely dense graph limits (even the more general $L^p$ limits) and Benjamini--Schramm limits (even in the stronger…
We consider the problem of covering an input graph $H$ with graphs from a fixed covering class $G$. The classical covering number of $H$ with respect to $G$ is the minimum number of graphs from $G$ needed to cover the edges of $H$ without…
We prove the following estimate for the spectrum of the normalized Laplace operator $\Delta$ on a finite graph $G$, \begin{equation*}1- (1- k[t])^{\frac{1}{t}}\leq \lambda_1 \leq \cdots \leq \lambda_{N-1}\leq 1+ (1- k[t])^{\frac{1}{t}},…
Let $\Gamma$ be a locally finite graph, $L$ the normalized Laplacian of $\Gamma$. If $\Gamma$ is uniformy locally finite, i.e. if each vertex has no more than $d$ adjacent vertices, then the matrix of $L$ (with respect to the standard…
A graph $G=(V,E)$ is a {\it unipolar graph} if there exits a partition $V=V_1 \cup V_2$ such that, $V_1$ is a clique and $V_2$ induces the disjoint union of cliques. The complement-closed class of {\it generalized split graphs} are those…
Extremal graph theory studies the maximum or minimum number of subgraphs isomorphic to a prescribed graph under given constraints. \textit{Localization} has recently emerged as a framework that refines such problems by assigning extremal…
The neighborhood degree list (NDL) is a graph invariant that refines information given by the degree sequence and joint degree matrix of a graph and is useful in distinguishing graphs having the same degree sequence. We show that the space…
We consider the graph whose vertex set is a conjugacy class ${\mathcal C}$ consisting of finite-rank self-adjoint operators on a complex Hilbert space $H$. The dimension of $H$ is assumed to be not less than $3$. In the case when operators…
An equitable coloring of a graph $G=(V,E)$ is a (proper) vertex-coloring of $G$, such that the sizes of any two color classes differ by at most one. In this paper, we consider the equitable coloring problem in block graphs. Recall that the…
In this paper, we first develop the theory of Musielak-Orlicz spaces on locally finite graphs, including completeness, reflexivity, separability, and so on. Then, we give some elementary properties of double phase operators on locally…
The notion of graph cover, also known as locally bijective homomorphism, is a discretization of covering spaces known from general topology. It is a pair of incidence-preserving vertex- and edge-mappings between two graphs, the…
Let P be a graph property. A graph is locally P if the subgraph induced by the open neighbourhood of every vertex has property P. A graph has the Dirac condition if the minimum degree of every vertex is at least half the order of the graph…
A recent example of a non-hyponormal injective composition operator in an $L^2$-space generating Stieltjes moment sequences, invented by three of the present authors, was built over a non-locally finite directed tree. The main goal of this…
In a graph, the switching operation reverses adjacencies between a subset of vertices and the others. For a hereditary graph class $\mathcal{G}$, we are concerned with the maximum subclass and the minimum superclass of $\mathcal{G}$ that…