Results 41 to 50 of about 45,743 (261)
Ramsey-nice families of graphs [PDF]
, 2018 For a finite family $\mathcal{F}$ of fixed graphs let $R_k(\mathcal{F})$ be the smallest integer $n$ for which every $k$-coloring of the edges of the complete graph $K_n$ yields a monochromatic copy of some $F\in\mathcal{F}$. We say that $\mathcal{F}$ is
Aharoni, Ron +7 more
core +2 more sources
Brooks' theorem with forbidden colors
Journal of Graph Theory, 2023 AbstractWe consider extensions of Brooks' classic theorem on vertex coloring where some colors cannot be used on certain vertices. In particular we prove that if is a connected graph with maximum degree that is not a complete graph and is a set of vertices where either at most colors are forbidden for every vertex in , and any two vertices of are
openaire +3 more sources
Graphs with $\chi=\Delta$ have big cliques
, 2015 Brooks' Theorem states that if a graph has $\Delta\ge 3$ and $\omega \le \Delta$, then $\chi \le \Delta$. Borodin and Kostochka conjectured that if $\Delta\ge 9$ and $\omega\le \Delta-1$, then $\chi\le \Delta-1$.
Cranston, Daniel W., Rabern, Landon
core +1 more source
Intrinsic metrics on graphs: A survey
, 2015 A few years ago various disparities for Laplacians on graphs and manifolds were discovered. The corresponding results are mostly related to volume growth in the context of unbounded geometry.
Keller, Matthias
core +1 more source
International Journal of Adaptive Control and Signal Processing, EarlyView.This work introduces an adaptive human pilot model that captures pilot time‐delay effects in adaptive control systems. The model enables the prediction of pilot–controller interactions, facilitating safer integration and improved design of adaptive controllers for piloted applications.
Abdullah Habboush, Yildiray Yildiz
wiley +1 more source
Advanced Functional Materials, EarlyView.A lack of standard approaches for testing and reporting the performance of metal halide perovskites and organic semiconductor radiation detectors has resulted in inconsistent interpretation of performance parameters, impeding progress in the field. This Perspective recommends key metrics and experimental details, which are suggested for reporting in ...
Jessie A. Posar +8 more
wiley +1 more source
Quantum Emitters in Hexagonal Boron Nitride: Principles, Engineering and Applications
Advanced Functional Materials, EarlyView.Quantum emitters in hexagonal boron nitride have emerged as a promising candidate for quantum information science. This review examines the fundamentals of these quantum emitters, including their level structures, defect engineering, and their possible chemical structures.
Thi Ngoc Anh Mai +8 more
wiley +1 more source
The Complexity of Distributed Edge Coloring with Small Palettes
, 2018 The complexity of distributed edge coloring depends heavily on the palette size as a function of the maximum degree $\Delta$. In this paper we explore the complexity of edge coloring in the LOCAL model in different palette size regimes. 1.
Chang, Yi-Jun +4 more
core +1 more source
Advanced Photonics Research, EarlyView.This review highlights recent advances in accelerating luminescence in nanostructures through cooperative emission, resonator coupling, and nonlocal light–matter interactions. By unifying concepts such as excitonic superradiance, superfluorescence, and the plasmonic Purcell effect, it reveals physical limits of ultrafast emission and their potential ...
Masaaki Ashida +3 more
wiley +1 more source
A Strengthening of Brooks' Theorem
Journal of Combinatorial Theory, Series B, 1999 This paper mainly proves the conjecture due to \textit{A. Beutelspacher} and \textit{P.-R. Hering} [Ars Comb. 18, 201-216 (1984; Zbl 0554.05025)]. More precisely, the author proves that for sufficiently large \(\Delta\), any graph with maximum degree at most \(\Delta\) and no cliques of size \(\Delta\) has a \(\Delta-1\) colouring.
openaire +2 more sources