Related papers: Region crossing change on planar trivalent graphs
The crossing number of a graph is the minimum number of double points over all generic immersions of the graph into the plane. In this paper we investigate the behavior of crossing number under a graph transformation, called $\mathsf{\Delta…
In this paper, we consider the problem of representing graphs by triangles whose sides touch. As a simple necessary condition, we show that pairs of vertices must have a small common neighborhood. On the positive side, we present linear…
A transitive decomposition of a graph is a partition of the edge or arc set giving a set of subgraphs which are preserved and permuted transitively by a group of automorphisms of the graph. In this paper we give some background to the study…
We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the behavior of a trajectory on a triangle tiling is described by…
We investigate the influence of spatial disorder correlations on smeared phase transitions, taking the quantum phase transition in itinerant magnets as an example. We find that even short-range correlations can have a dramatic effect and…
We study a mean field model of a complex network, focusing on edge and triangle densities. Our first result is the derivation of a variational characterization of the entropy density, compatible with the infinite node limit. We then…
The modeling of risk situations that occur in a space-time framework can be done using max-stable random fields on lattices. Although the summary coefficients for the spatial and temporal behaviour do not characterize the finite-dimensional…
This paper presents an analysis on the effects of floating-point arithmetic on the constructing bifurcation diagram of the quadratic map. More precisely, we are interested in showing the dependence of initial conditions to obtain some…
Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of…
We discuss the effect of noise on a system with a quasi-periodicity of different dimensions. As the basic model of our research we use the simplest three-dimensional map with two-frequency and three-frequency quasi-periodicity. Modification…
We introduce virtual tribrackets, an algebraic structure for coloring regions in the planar complement of an oriented virtual knot or link diagram. We use these structures to define counting invariants of virtual knots and links and provide…
3-list colouring is an NP-complete decision problem. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving 3-list colouring on permutation graphs.
The short-time Fourier transform (STFT) is widely used to analyze the spectra of temporal signals that vary through time. Signals defined over graphs, due to their intrinsic complexity, exhibit large variations in their patterns. In this…
This article deals with the study of the birational transformations of the projective complex plane which leave invariant an irreducible algebraic curve. We try to describe the state of art and provide some new results on this subject.
Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrary planar graph to index the decomposition. We prove that…
I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…
We investigate the problem of drawing graphs in 2D and 3D such that their edges (or only their vertices) can be covered by few lines or planes. We insist on straight-line edges and crossing-free drawings. This problem has many connections…
We show how the spectrum of a graph Laplacian changes with respect to a certain type of rank-one perturbation. We apply our finding to give new short proofs of the spectral version of Kirchhoff's Matrix Tree Theorem and known derivations…
The asymptotic study of percolation on finite transitive graphs is considered. Several questions and very few answers regarding percolation on finite graphs are presented.
A theoretical and experimental analysis is made of the effects of self-adaptation in a simple evolving system. Specifically, we consider the effects of coding the mutation and crossover probabilities of a genetic algorithm evolving in…