Related papers: Rainbow Thresholds
The paper is devoted to the properties of the Lagrange spectrum left endpoints and so-called attainable numbers.
A conjecture of Talagrand (2010) states that the so-called expectation and fractional expectation thresholds are always within at most some constant factor from each other. Expectation (resp. fractional expectation) threshold $q$ (resp.…
An edge-coloured graph is said to be rainbow if no colour appears more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decade as they capture the essence of a number of interesting…
Analytic results for the threshold and pseudothreshold values of the sunset diagram with arbitrary masses are obtained in terms of dilogarithms of ratios of the masses.
The present status of superstring phenomenology is briefly discussed.
We give upper and lower bounds of perturbation series for transition densities, corresponding to additive gradient perturbations satisfying certain space-time integrability conditions.
The physics potential of the next generation of Gamma Ray Telescopes in exploring the Gamma Ray Horizon is discussed. It is shown that the reduction in the Gamma Ray detection threshold might open the window to use precise determinations of…
In this short note, we present a purely entropic proof that in a $3$-edge-colored simple graph with $R$ red edges, $G$ green edges, and $B$ blue edges, the number of rainbow triangles is at most $\sqrt{2RGB}$.
We present a short review on the recent progresses that have been made in meson spectroscopy. We discuss the experimental discoveries made at the BaBar and Belle experiments, as well as the possible interpretations of the new resonances.
We discuss recent progress in understanding the effects of certain trapping geometries on cut-off resolvent estimates, and thus on the qualititative behavior of linear evolution equations. We focus on trapping that is unstable, so that…
Interval analysis, when applied to the so called problem of experimental data fitting, appears to be still in its infancy. Sometimes, partly because of the unrivaled reliability of interval methods, we do not obtain any results at all.…
A spanning tree of a properly edge-colored complete graph, $K_n$, is rainbow provided that each of its edges receives a distinct color. In 1996, Brualdi and Hollingsworth conjectured that if $K_{2m}$ is properly $(2m-1)$-edge-colored, then…
We show that there is an unexpected relation between free divisors and stability and coincidence thresholds for projective hypersurfaces.
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.
In this paper we present some new upper bounds of the Cusa-Huygens and the Huygens approximations. Bounds are obtained in the forms of some polynomial and some rational functions.
The work deals with the threshold probablity for r-colorability in the binomial model H(n,k,p) of a random k-uniform hypergraph. We prove a lower bound for this threshold which improves the previously known results in the wide range of the…
Parameterised subgraph counting problems are the most thoroughly studied topic in the theory of parameterised counting, and there has been significant recent progress in this area. Many of the existing tractability results for parameterised…
We present a review of selected topics concerning the creation and evolution of child universes, together with a concise account of some recent progress in the field.
When many colors appear in edge-colored graphs, it is only natural to expect rainbow subgraphs to appear. This anti-Ramsey problem has been studied thoroughly and yet there remain many gaps in the literature. Expanding upon classical and…
Given graphs $G_1,\ldots,G_s$ all on the same vertex set and a graph $H$ with $e(H) \leq s$, a copy of $H$ is transversal or rainbow if it contains at most one edge from each $G_c$. When $s=e(H)$, such a copy contains exactly one edge from…