Mathematics for Computer Science

11.11. Forests & Trees 333 edge is removed, no path remains, and so the graph is not connected. Since the tree has at least ...

Chapter 11 Simple Graphs334 Figure 11.22 A graph where the edges of a spanning tree have been thickened. minimum-edge spanning s ...

11.11. Forests & Trees 335 2 3 3 7 1 2 1 (a) 2 3 3 7 1 2 1 4 1 1 3 (b) Figure 11.23 A spanning tree (a) with weight 19 for a ...

Chapter 11 Simple Graphs336 Ifeis an edge ofGandSis a spanning subgraph, we’ll writeSCefor the spanning subgraph with edgesE.S/[ ...

11.11. Forests & Trees 337 2 7 1 2 1 1 3 Figure 11.25 A spanning tree found by Algorithm 1. Algorithm 2.Grow a forest one ed ...

Chapter 11 Simple Graphs338 by suitable tie-breaking. The coloring that explains Algorithm 1 also justifies a more flexible algo ...

11.11. Forests & Trees 339  Another interesting fact falls out of the proof of Lemma 11.11.10: Corollary 11.11.11.If all ed ...

Chapter 11 Simple Graphs340 the population would change the averages. If he knew graph theory, the researcher would realize that ...

11.11. Forests & Trees 341 1 2 4 3 5 6 7 8 9 10 (a)G 1 1 2 4 3 5 6 8 9 7 10 (b)G 2 1 2 4 3 5 6 8 9 7 10 (c)G 3 1 2 3 4 6 5 8 ...

Chapter 11 Simple Graphs342 Problem 11.5. (a)For any vertex,v, in a graph, letN.v/be the set ofneighbors ofv, namely, the vertic ...

11.11. Forests & Trees 343 Sure enough, this is a line graph. Inductive case:We assume that the induction hypothesis holds f ...

Chapter 11 Simple Graphs344 seen by the Student Association. Each eligible club would like to delegate one of its members to app ...

11.11. Forests & Trees 345 For example, here is a 4  4 Latin square: 1 2 3 4 3 4 2 1 2 1 4 3 4 3 1 2 (a)Here are three rows ...

Chapter 11 Simple Graphs346 Problem 11.11. Because of the incredible popularity of Math for Computer Science, Rajeev decides to ...

11.11. Forests & Trees 347 each student so that every student is unique at the end of the term as well. Suggestion: Use Hall ...

Chapter 11 Simple Graphs348 Class Problems Problem 11.16. Consider a stable marriage problem with 4 boys and 4 girls and the fol ...

11.11. Forests & Trees 349 Homework Problems Problem 11.18. The most famous application of stable matching was in assigning ...

Chapter 11 Simple Graphs350 Problems for Section 11.7 Class Problems Problem 11.21. LetGbe the graph below^11. Carefully explain ...

11.11. Forests & Trees 351 (a)Recast this problem as a question about coloring the vertices of a particular graph. Draw the ...

Chapter 11 Simple Graphs352 Inductive step: We may assumeP.n/. To proveP.nC1/, letGnC 1 be a graph withnC 1 vertices whose verte ...