Question+ Let T be a tree. Prove, direct from the definition of tree, that: (a) Every edge of T is a bridge. Hint: If a...
Question 1# (a) Let G be a connected graph and C a non-trivial circuit in G. Prove directly that if an edge e fa, b is removed from C then the subgraph S C G that remains is still connected. "Directly' means using only the definitions of the concepts involved, in this case connected' and 'circuit'. Hint: If z and y are vertices of G connected by path that includes e, is there an alternative path connecting x to y...
Problem 3: Bounded-Degree Spanning Trees (10 points). Recall the minimum spanning tree problem studied in class. We define a variant of the problem in which we are no longer concerned with the total cost of the spanning tree, but rather with the maximum degree of any vertex in the tree. Formally, given an undirected graph G = (V,E) and T ⊆ E, we say T is a k-degree spanning tree of G if T is a spanning tree of G,...
Let S be a string that ends with a distinct end symbol S. In the suffix tree for S, each edge is labeled by a substring of S. For any node u, we use path(u) to denote the string formed by concatenating the labels of the edges along the path from root to u. For instance, path(root), the empty string. And for any leaf ls a suffix of S in the suffix tree, path(e) For two internal nodes u and...
Let T be a tree with 3 or more vertices. Prove the following: (a) There must be two vertices v, w in T that are not adjacent. (b) If T′ is the graph obtained from T by adding a new edge joining v to w, then T′ is not a tree.
er (a) Let G be a connected graph and C a non-trivial circuit in G. Prove directly that if an edge ={a, b} is removed from then the subgraph S CG that remains is still connected. Directly' means using only the definitions of the concepts involved, in this case 'connected' and 'circuit'. Hint: If r and y are vertices of G connected by path that includes e, is there an alternative path connecting x to y that avoids e? (b)...
Say that we have an undirected graph G(V, E) and a pair of vertices s, t and a vertex v that we call a a desired middle vertex . We wish to find out if there exists a simple path (every vertex appears at most once) from s to t that goes via v. Create a flow network by making v a source. Add a new vertex Z as a sink. Join s, t with two directed edges of capacity...
please help me make this into a contradiction or a direct proof please. i put the question, my answer, and the textbook i used. thank you also please write neatly proof 2.5 Prove har a Simple sraph and 13 cdges cannot be bipartite CHint ercattne gr apn in to ertex Sets and Court tne忤of edges Claim Splitting the graph into two vertex, Sets ves you a 8 Ver ices So if we Change tne书 apn and an A bipartite graph...
1. (25) [Maximum bottleneck rate spanning treel] Textbook Exercise 19 in Chapter 4. Given a connected graph, the problem is to find a spanning tree in which every pair of nodes has a maximum bottleneck rate path between the pair. (Note that the bottleneck rate of a path is defined as the minimum bandwidth of any edge on the path.) First give the algorithm (a sketch of the idea would be sufficient), and then prove the optimality of the algorithm....
In this question, we will think about how to answer shortest path problems where we have more than just a single source and destination. Answer each of the following in English (not code or pseudocode). Each subpart requires at most a few sentences to answer. Answers significantly longer than required will not receive full credit You are in charge of routing ambulances to emergency calls. You have k ambulances in your fleet that are parked at different locations, and you...
C++ Binary Search Tree question. I heed help with the level 2 question please, as level 1 is already completed. I will rate the answer a 100% thumbs up. I really appreciate the help!. Thank you! searching.cpp #include <getopt.h> #include <iostream> #include <sstream> #include <stdlib.h> #include <unistd.h> using namespace std; // global variable for tree operations // use to control tree maintenance operations enum Mode { simple, randomised, avl } mode; // tree type // returns size of tree //...