An Unavoidable Set of D-Reducible Configurations
نویسنده
چکیده
We give a new proof of the four-color theorem by exhibiting an unavoidable set of 2822 D-reducible configurations. The existence of such a set had been conjectured by several researchers including Stromquist [18], Appel and Haken [2] and Robertson, Sanders, Seymour and Thomas [15].
منابع مشابه
On the reducible $M$-ideals in Banach spaces
The object of the investigation is to study reducible $M$-ideals in Banach spaces. It is shown that if the number of $M$-ideals in a Banach space $X$ is $n(<infty)$, then the number of reducible $M$-ideals does not exceed of $frac{(n-2)(n-3)}{2}$. Moreover, given a compact metric space $X$, we obtain a general form of a reducible $M$-ideal in the space $C(X)$ of continuous functions on $X$. The...
متن کاملLaudal Type Theorems for Algebraic Curves
Laudal’s Lemma states that if C is an integral curve in P3 of degree d > s2 + 1 and Z is its general plane section, then C is contained in a surface of degree s provided that Z is contained in a curve of degree s. The aim of this paper is to extend Laudal’s Lemma to possibly reducible curves proving that, under the unavoidable hypothesis that the Hilbert function of the generic plane section is...
متن کاملInstitutional Analysis of Corruption Configurations in South-West Asian Countries: A Fuzzy-Set Qualitative Comparative Analysis (fsQCA)
Considering corruption as one of the chronic harms of the administrative system,and the social factor affecting economic growth, the present study sought toexplain, for the first time, the differences in the perceived levels of corruptionamong 16 Southwest Asian countries, relying on the sociological “newinstitutionalism” theory in analyzing organizations, describing cau...
متن کاملConcurrent vector fields on Finsler spaces
In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fields. We also prove that an L-reducible Finsler metric admitting a concurrent vector field reduces to a Landsberg metric.In this paper, we prove that a non-Riemannian isotropic Berwald metric or a non-Riemannian (α,β) -metric admits no concurrent vector fi...
متن کاملPerformance Evaluation of Magnetorheological Damper Valve Configurations Using Finite Element Method
The main purpose of this paper is to study various configurations of a magnetorheological (MR) damper valve and to evaluate their performance indices typically dynamic range, valve ratio, inductive time constant and pressure drop. It is known that these performance indices (PI) of the damper depend upon the magnetic circuit design of the valve. Hence, nine valve configurations are considered fo...
متن کامل