Related papers: Region crossing change on planar trivalent graphs
In this paper we consider graphs whose edges are associated with a degree of {\em importance}, which may depend on the type of connections they represent or on how recently they appeared in the scene, in a streaming setting. The goal is to…
This article is devoted to the properties of the planar triangulations. The conjugated planar triangulation will be introduced and on the base of the properties, which were achieved by the other authors there will be proved some theorems,…
The interaction between electrons and plasmons in trilayer graphene is investigated within the Overhauser approach resulting in the 'plasmaron' quasi-particle. This interaction is cast into a field theoretical problem, nd its effect on the…
The \emph{segment number} of a planar graph is the smallest number of line segments whose union represents a crossing-free straight-line drawing of the given graph in the plane. The segment number is a measure for the visual complexity of a…
In this paper, we prove that the crossing number of circulant graph $C(3k+1;\{1,k\})$ on the projective plane is $k$ for $k \geq 3$.
The properties of the spectrum of the overlap Dirac operator and their relation to random matrix theory are studied. In particular, the predictions from chiral random matrix theory in topologically non-trivial gauge field sectors are…
We study the depinning transition of driven interfaces in thin ferromagnetic films driven by external magnetic fields. Approaching the transition point the correlation length increases with decreasing driving. If the correlation length…
We generalize the Five Color Theorem by showing that it extends to graphs with two crossings. Furthermore, we show that if a graph has three crossings, but does not contain K_6 as a subgraph, then it is also 5-colorable. We also consider…
We study the effect of sudden transitions in the effective Planck mass during inflation on primordial power spectra. Specifically, we consider models in which this variation results from the non-minimal coupling of a Brans-Dicke type scalar…
A graph is near-planar if it can be obtained from a planar graph by adding an edge. We show the surprising fact that it is NP-hard to compute the crossing number of near-planar graphs. A graph is 1-planar if it has a drawing where every…
Recently, transformer architectures for graphs emerged as an alternative to established techniques for machine learning with graphs, such as (message-passing) graph neural networks. So far, they have shown promising empirical results, e.g.,…
This paper examines the existence and region of convergence of Fourier transform of the functions of bicomplex variables with the help of projection on its idempotent components as auxiliary complex planes. Several basic properties of this…
In this paper we study the structure of the graphs associated with the iterations of the map $x \mapsto x+x^{-1}$ over finite fields of characteristic three.
We investigate the propagation of surface waves along a spatially dispersive graphene sheet, including substrate effects. The proposed analysis derives the admittances of an equivalent circuit of graphene able to handle spatial dispersion,…
The effect of a random surface field, within the bimodal distribution, on the layering transitions in a spin-1/2 Ising thin film is investigated, using Monte Carlo simulations. It is found that the layering transitions depend strongly on…
It is shown how simple assumptions lead to piecewise linear behavior, which is observed in certain phase transitions.
We venture a proof of crossing symmetry for non-planar diagrams in perturbative QFT. For the planar diagrams a proof of crossing is available in the literature and our method closely follows the one depicted in that case. We classify the…
We construct a new family of trivalent expanders tessellating hyperbolic surfaces with large isometry groups. These graphs are obtained from a family of Cayley graphs of nilpotent groups via $(\Delta-Y)$-transformations. We compare this…
We study the spectra and damping of surface plasmon-polaritons in double graphene layer structures. It is shown that application of bias voltage between layers shifts the edge of plasmon absorption associated with the interband transitions.…
We study graphs that are formed by independently-positioned needles (i.e., line segments) in the unit square. To mathematically characterize the graph structure, we derive the probability that two line segments intersect and determine…