We show that if the graph of a bounded analytic function in the unit disk D is not complete pluripolar in C then the projection of the closure of its pluripolar hull contains a fine neighborhood of a point p ∈ ∂D. On the other hand we show that if an analytic function f in D extends to a function F which is defined on a fine neighborhood of a point p ∈ ∂D and is finely analytic at p then the pl...

Graph convolutional neural networks exploit convolution operators, based on some neighborhood aggregating scheme, to compute representations of graphs. The most common operators only local topological information. To consider wider receptive fields, the mainstream approach is non-linearly stack multiple graph (GC) layers. In this way, however, interactions among GC parameters at different level...

For every k ∈ N0, we consider graphs G where for every induced subgraph H of G, ∆(H) ≤ χ(H) − 1 + k holds, where ∆(H) is the maximum degree and χ(H) is the chromatic number of the subgraph H . Let us call this family of graphs Υk. We give a finite forbidden induced subgraph characterization of Υk for every k. We compare these results with those given in On bounding the difference between the ma...

Combining the concept of a fractional ( g , f )-covered graph with that ID-( )-factor-critical graph, we define covered graph. This paper reveals relationship between some parameters and existence graphs. A sufficient condition for being is presented. In addition, demonstrate sharpness main result in this by constructing special class. Furthermore, other parameters(such as binding number, tough...

Point-based shape representation has received increased attention in recent years, mainly due to its simplicity. One of the most fundamental operations for point set processing is to find the neighbors of each point. To do this, mesh structures and neighborhood graphs are commonly used. However, though meshes are very popular in the field of computer graphics, neighbor relations encoded in a me...

We prove that every triangle-free planar graph with minimum degree 3 has radius at least 3; equivalently, no vertex neighborhood is a dominating set.

Graph grammars and graph transformation systems [9] have turned out to be applicable for solving various problems of recent computer science [3][4]. It is also known, however, that pure graph grammars are often no suitable solutions for practical problems, because graph grammar derivations (as any grammar derivations) are of non-deterministic nature whilst deterministic and predictable behavior...

In this paper we provide concrete combinatorial formal deformation algorithms, namely sequences of elementary collapses and expansions, which relate various previously extensively studied families of combinatorially defined polyhedral complexes. To start with, we give a sequence of elementary collapses leading from the barycentric subdivision of the neighborhood complex to the Lovász complex of...

We introduce the notion of locally identifying coloring of a graph. A proper vertex-coloring c of a graph G is said to be locally identifying, if for any adjacent vertices u and v with distinct closed neighborhood, the sets of colors that appear in the closed neighborhood of u and v are distinct. Let χlid(G) be the minimum number of colors used in a locally identifying vertex-coloring of G. In ...

β-skeletons, a prominent member of the neighborhood graph family, have interesting geometric properties and various applications ranging from geographic networks to archeology. This paper focuses on developing a new, more general than the present one, definition of β-skeletons based only on the distance criterion. It allows us to consider them in many different cases, e.g. for weighted graphs o...