这学期选了晴宝开的随机算法,lecture 5 介绍了几个组合问题的概率方法,有个例子感觉挺有趣的。 对于图 G ,我们定义其周长 (Girth) 为最小环长度,染色数 (Chromatic Number) 为最小的颜色数,使得存在一种合法的点染色方法。 一个图的点染色方法称作是合法,当且仅当每条边两端的颜色不同。 定理:对于任意的 ...
P. Erd˝os, Graph theory and probability, Canad. J. Math. 11 (1959), 34-38.Graph Theory and Probability - Erdős - 1959 () Citation Context ...oyed with uniform distribution, i.e., { d 1 if x ∈ [−1/2, 1/2] , fU(x) := 0 otherwise. inria-00364370, version 1 ...
The introduction of probabilistic methods in graph theory, especially in the study of Erdős and Rényi of the asymptotic probability of graph connectivity, gave rise to yet another branch, known as random graph theory, which has been a fruitful source of graph-theoretic results.哥尼斯堡大桥问题...
P. Erdős: Graph Theory and Probability, II. Canad. Journal of Math., 13 (1961) 346–352. Article Google Scholar P. Erdős: On a theorem of Rademacher-Turán, Illinois J. Math., 6 (1962) 122–127. (Reprinted in [60].) Google Scholar P. Erdős: Über ein Extremalproblem ...
Probability map model as a perfect combination of graph theory and probability theory, probability models with graphical representation, Visual reasoning, applied to expression and analysis of uncertainties and probabilities of things, uncertainty more effectively in the knowledge-based reasoning. ...
Random graphs are ubiquitous in modern probability theory. Besides their intrinsic mathematical beauty, they are also used to model complex networks. In the early 2000’s, I. Benjamini and O. Schramm introduced a mathematical framework in which they endowed the set of locally finite rooted connecte...
Theoretical or Mathematical/ graph theoryprobability/ probabilistic methodgraphedge-transitivesubgraphsisomorphic/ B0240 Probability and statistics B0250 Combinatorial mathematics C1140 Probability and statistics C1160 Combinatorial mathematicsWe show that a simple graph U is edge-transitive if and only if it...
Models are extremely important in modern network theory. It can be argued that the discovery of models for very large networks with a mixture of randomness and order lies at the heart of the transition from conventional graph theory to the modern science of networks. Here we describe three prot...
Combinatorics - Graph Theory, Counting, Probability: A graph G is said to be planar if it can be represented on a plane in such a fashion that the vertices are all distinct points, the edges are simple curves, and no two edges meet one another except at
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