19th Ave New York, NY 95822, USA

# 数学代写|图论作业代写Graph Theory代考|Specialized classes of intersection graphs

my-assignmentexpert™ 图论graph theory作业代写，免费提交作业要求， 满意后付款，成绩80\%以下全额退款，安全省心无顾虑。专业硕 博写手团队，所有订单可靠准时，保证 100% 原创。my-assignmentexpert™， 最高质量的图论graph theory作业代写，服务覆盖北美、欧洲、澳洲等 国家。 在代写价格方面，考虑到同学们的经济条件，在保障代写质量的前提下，我们为客户提供最合理的价格。 由于统计Statistics作业种类很多，同时其中的大部分作业在字数上都没有具体要求，因此图论graph theory作业代写的价格不固定。通常在经济学专家查看完作业要求之后会给出报价。作业难度和截止日期对价格也有很大的影响。

my-assignmentexpert™ 为您的留学生涯保驾护航 在数学Mathematics作业代写方面已经树立了自己的口碑, 保证靠谱, 高质且原创的数学Mathematics代写服务。我们的专家在图论graph theory代写方面经验极为丰富，各种图论graph theory相关的作业也就用不着 说。

## 数学代写|图论作业代写Graph Theory代考|Tolerance graphs

Tolerance graphs were introduced in 1982 as a natural extension of interval graphs. Each vertex is associated with an interval on the real line and a positive number called its tolerance. A tolerance is considered unbounded if it exceeds the length of the interval. Two vertices are adjacent if and only if the length of the intersection of their associated intervals is not less than the tolerance of one of them. We can think of two meetings that are set to overlap in time, yet are assigned to the same meeting room. In the interval graph model they conflict; in the tolerance model, if both are sufficiently tolerant, they do not.

This tolerance-conflict model set the stage for decades of further research on multiple themes – special families of tolerance graphs and their properties, directed graph versions, generalizations beyond intervals and restricted models. All of these involve some notion of measured intersection, known as tolerance. We have bounded, proper and unit tolerance graphs, several types of tree tolerance graphs, rank tolerance graphs , Archimedean $\phi$-tolerance graphs and others .
The computational complexity of recognizing tolerance graphs and bounded tolerance graphs had remained open for 28 years. Hayward and Shamir showed that the problem is in NP, and Mertzios, Sau and Zaks , proved that it is NP-hard. Thus we have the following result.

## 数学代写|图论作业代写Graph Theory代考|Tolerance graphs on trees

Let T be a tree and let $\left{T_{i}\right}$ be a collection of subtrees (connected subgraphs) of $T$. We may think of the host tree $T$ as either
(1) a continuous model of a tree embedded in the plane, thus generalizing the real line from the 1-dimensional case, or
(2) a finite discrete model of a tree, a connected graph of vertices and edges having no cycles, thus generalizing the graph $P_{k}$ from the 1-dimensional case.

The distinction between these two models becomes important when measuring the size of the intersection of two subtrees. For example, in the continuous model (1), we might take the size of the intersection to be the length of a longest common path of the two subtrees measured along the host tree . In the discrete model , we might count the number of common vertices or common edges. Typically, one uses the expressions ‘non-empty intersection’ or ‘vertex-intersection’ to mean sharing a vertex of $T$ (or a point, in the continuous model), and ‘non-trivial intersection’ or ‘edge-intersection’ to mean sharing an edge or otherwise measurable segment of $T$. In this way, edge-intersection is more tolerant than vertex-intersection. Using this terminology, we have the following classical result of Buneman, Gavril and Walter.

## 数学代写|图论作业代写GRAPH THEORY代考|Intersection graphs of paths on a grid

We conclude this section with another pair of graph classes that contrast the difference between vertex-intersection and edge-intersection, this time with paths on a grid. They were motivated by applications in circuit layout and chip manufacturing, but could be equally applied to traffic routing, scheduling and other natural problems.

A vertex-intersection graph of paths on a grid or VPG graph is a graph for which there exists a family of paths on a grid in one-one correspondence with its vertex-set for which two vertices are adjacent if and only if the corresponding paths share at least one grid-point. An edge-intersection graph of paths on a grid or E P G graph, is defined similarly, with the exception that two vertices are adjacent if and only if the corresponding paths share at least one grid-edge. A recent survey on EPG graphs appears in .

## 数学代写|图论作业代写GRAPH THEORY代考|TOLERANCE GRAPHS ON TREES

1嵌入平面中的树的连续模型，从而从一维情况推广实线，或
2树的有限离散模型，没有环的顶点和边的连通图，从而推广了图磷ķ从一维情况。

## Matlab代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。