MIT6_042JS10_lec20_prob

MIT6_042JS10_lec20_prob - Massachusetts Institute of...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science March 19 Prof. Albert R. Meyer revised March 12, 2010, 1326 minutes In-Class Problems Week 7, Fri. Problem 1. Figures 1–4 show different pictures of planar graphs. 1 a b c d Figure 1 a b c d Figure 2 a b c d e Figure 3 a b c d e Figure 4 Creative Commons 2010, Prof. Albert R. Meyer .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 In-Class Problems Week 7, Fri. (a) For each picture, describe its discrete faces (simple cycles that define the region borders). (b) Which of the pictured graphs are isomorphic? Which pictures represent the same planar em- bedding ? – that is, they have the same discrete faces. (c) Describe a way to construct the embedding in Figure 4 according to the recursive Defini- tion 12.3.1 of planar embedding. For each application of a constructor rule, be sure to indicate the faces (cycles) to which the rule was applied and the cycles which result from the application. Problem 2. Prove the following assertions by structural induction on the definition of planar embedding. (a) In a planar embedding of a graph, each edge is traversed a total of two times by the faces of the embedding. (b)
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

MIT6_042JS10_lec20_prob - Massachusetts Institute of...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online