Chapter 11: Q29E (page 796)
Explain how backtracking can be used to find a Hamilton path or circuit in a graph.
By using the backtracking process, it can get Hamilton path circuit in a graph.
Over 22 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
How many vertices, leaves, and internal vertices does the rooted Fibonacci tree \({T_n}\) have, where \(n\) is a positive integer? What is its height?
Show that if there are \(r\) trees in the forest at some intermediate step of Sollin’s algorithm, then at least \(\left\lceil {\frac{r}{2}} \right\rceil \)edges are added by the next iteration of the algorithm.
Show that every tree can be colored using two colors. The rooted Fibonacci trees \({\bf{Tn}}\) are defined recursively in the following way. \({\bf{T1}}\)and\({\bf{T}}2\) are both the rooted tree consisting of a single vertex, and for \({\bf{n = 3, 4,}}...{\bf{,}}\) the rooted tree \({\bf{Tn}}\) is constructed from a root with \({\bf{Tn - }}1\) as its left subtree and \({\bf{Tn - 2}}\) as its right subtree.
Suppose that \({{\bf{d}}_{\bf{1}}}{\bf{,}}{{\bf{d}}_{\bf{2}}}{\bf{,}}...{\bf{,}}{{\bf{d}}_{\bf{n}}}\) are n positive integers with sum \({\bf{2n - 2}}\). Show that there is a tree that has n vertices such that the degrees of these vertices are \({{\bf{d}}_{\bf{1}}}{\bf{,}}{{\bf{d}}_{\bf{2}}}{\bf{,}}...{\bf{,}}{{\bf{d}}_{\bf{n}}}\).
Find the second least expensive communications network connecting the five computer centers in the problem posed at the beginning of the section.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
