Δ+300\Delta+300 is a Bound on the Adjacent Vertex Distinguishing Edge Chromatic Number

An adjacent vertex distinguishing edge-coloring or an \avd-coloring of a simple graph $G$ is a proper edge-coloring of $G$ such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree $\Delta$ and with no isolated edges has an \avd-coloring with at most $\Delta+300$ colors, provided that $\Delta >10^{20}$

Graph Colorings with Constraints

A graph is a collection of vertices and edges, often represented by points and connecting lines in the plane. A proper coloring of the graph assigns colors to the vertices, edges, or both so that proximal elements are assigned distinct colors. Here we examine results from three different coloring problems. First, adjacent vertex distinguishing total colorings are proper total colorings such that the set of colors appearing at each vertex is distinct for every pair of adjacent vertices. Next, vertex coloring total weightings are an assignment of weights to the vertices and edges of a graph so that every pair of adjacent vertices have distinct weight sums. Finally, edge list multi-colorings consider assignments of color lists and demands to edges; edges are colored with a subset of their color list of size equal to its color demand so that adjacent edges have disjoint sets. Here, color sets consisting of measurable sets are considered

Symmetry in Graph Theory

This book contains the successful invited submissions to a Special Issue of Symmetry on the subject of ""Graph Theory"". Although symmetry has always played an important role in Graph Theory, in recent years, this role has increased significantly in several branches of this field, including but not limited to Gromov hyperbolic graphs, the metric dimension of graphs, domination theory, and topological indices. This Special Issue includes contributions addressing new results on these topics, both from a theoretical and an applied point of view

New Directions in Geometric and Applied Knot Theory

The aim of this book is to present recent results in both theoretical and applied knot theory—which are at the same time stimulating for leading researchers in the field as well as accessible to non-experts. The book comprises recent research results while covering a wide range of different sub-disciplines, such as the young field of geometric knot theory, combinatorial knot theory, as well as applications in microbiology and theoretical physics

Dielectron Production in Heavy Ion Collisions at 158 GeV/c per Nucleon

In this paper, the low-mass electron pair production in 158 AGeV/c Pb-Au collisions is investigated with the Cherenkov Ring Electron Spectrometer (CERES) at the Super Proton Synchrotron accelerator (SPS) at CERN. The main goal is to search for modifications of hadron properties in hot and dense nuclear matter. The presented re-analysis of the 1996 data set is focused on a detailed study of the combinatorial-background subtraction by means of the mixed-event technique. The results confirm previous findings of CERES. The dielectron production in the mass range of 0.25<m(ee)<2GeV/c**2 is enhanced by a factor of 3.0+-1.3(stat.)+-1.2(syst.) over the expectation from neutral meson decays. The data is compared to transport model calculations and seem to favor the version including in-medium effects. Furthermore, the development of a new technology to manufacture ultralightweight mirrors for Ring Imaging Cherenkov detectors (RICH) is described. Replacement of the RICH-2 glass mirror by a mirror almost transparent to electrons would considerably improve the performance of the upgraded CERES detector system including a radial Time Projection Chamber (TPC).Comment: 152 pages, 142 figures, published in http://elib.tu-darmstadt.de/diss/00019

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum