1北京邮电大学计算机学院--离散数学-10.7-planargraph.ppt

1北京邮电大学计算机学院--离散数学-10.7-planargraph.ppt

  1. 1、本文档共31页,可阅读全部内容。
  2. 2、有哪些信誉好的足球投注网站(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
  3. 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载
  4. 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
1北京邮电大学计算机学院--离散数学-10.7-planargraph.ppt

* * College of Computer Science Technology, BUPT Homework 设G是连通平面图,G的每个面的度数大于等于l (l ? 3),则 e ? l(v-2)/(l-2) 用上述性质证明K3,3不是平面图。 §10.7 6, 8, 12, 18, 24, 30 College of Computer Science Technology, BUPT Yang Juan yangjuan@bupt.edu.cn College of Computer Science Technology Beijing University of Posts Telecommunications Discrete Mathematical Structures Planar Graphs * * College of Computer Science Technology, BUPT Planar Graphs – 平面图 A graph is called planar if it can be drawn in the plane in such a way that no two edges cross. Example of a planar graph: The clique on 4 nodes. * * College of Computer Science Technology, BUPT Is K5 planar? * * College of Computer Science Technology, BUPT What about K3,3 ? * * College of Computer Science Technology, BUPT Why Planar? The problem of drawing a graph in the plane arises frequently in VLSI layout problems. * * College of Computer Science Technology, BUPT Regions, faces – 面 A planar representation of a graph splits the plane into regions that we call faces, including an unbounded region. one face two faces * * College of Computer Science Technology, BUPT Question Can you redraw this graph as a planar graph so as to alter the number of its faces? * * College of Computer Science Technology, BUPT Example This graph has 6 vertices 8 edges and 4 faces vertices – edges + faces = 2 * * College of Computer Science Technology, BUPT Example This graph has 7 vertices 12 edges and 7 faces vertices – edges + faces = 2 * * College of Computer Science Technology, BUPT Euler Theorem 1752 Let G be a connected planar simple graph with e edges and v vertices. Let r be the number of regions in a planar representation of G. Then r = e ? v +2. * * College of Computer Science Technology, BUPT Proof: By induction on the # of cycles of G. Base case: G has no cycles. G is connected so it must be a tree. Thus, e = v - 1 and r = 1. * * College of Computer Science Technology, BUPT Inductive step Suppose G has at least one

文档评论(0)

heroliuguan + 关注
实名认证
内容提供者

该用户很懒,什么也没介绍

版权声明书
用户编号:8073070133000003

1亿VIP精品文档

相关文档