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. Erdo˝s, "Graph theory and probability", Canad. J. Math. 11 (1959), 34-38.Graph Theory and Probability - Erdo虌s - 1959 () Citation Context ...es that are first-order decidable ([3, 20, 37]). For general relational structures, finite dualities were characterized in [34] ...
Graph theory is also used to study molecules in chemistry and physics. In condensed matter physics, the three-dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms. In chem...
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
Graph theory and probability. II Define f (k, l) as the least integer so that every graph having f (k, 1) vertices contains either a complete graph of order k or a set of l independent vertices (a complete graph of order k is a graph of k vertices every two of which are... ...
The theory of random graphs lies at the intersection between graph theory and probability theory, and studies the properties of typical random graphs. A random graph is obtained by starting with a set of n vertices and adding edges between them at random. Different random graph models produce ...
It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics...
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...
/σ. Calculators have now all but eliminated the use of such tables. For further detailsseeprobability theory. Britannica Quiz Numbers and Mathematics The term “Gaussian distribution” refers to the German mathematicianCarl Friedrich Gauss, who first developed a two-parameterexponentialfunction in 1809...
我们继续上一节的内容 Speechless:Graph Decomposition [Extremal graph theory]图分解系列1主要讨论 超图分解( Hypergraph decomposition)。令 G,F 为 k -一致超图, G 有 F 分解的概念与图上的分解类似。 首先…