Say that G contains an Euler Cycle. Show that for every bi-connected component X so that v ∈ X, |E(X, v)| is even.
WARNING: I REPORT copy & paste answers. Don't risk it.
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Say that G contains an Euler Cycle. Show that for every bi-connected component X so that...
Question 1: Given an undirected connected graph so that every edge belongs to at least one simple cycle (a cycle is simple if be vertex appears more than once). Show that we can give a direction to every edge so that the graph will be strongly connected. Question 2: Given a graph G(V, E) a set I is an independent set if for every uv el, u #v, uv & E. A Matching is a collection of edges {ei} so...
Long paths we show that for every n ≥ 3 if deg(v) ≥ n/2 for every v ∈ V then the graph contains a simple cycle (no vertex appears twice) that contains all vertices. Such a path is called an Hamiltonian path. From now on we assume that deg(v) ≥ n/2 for every v. 1. Show that the graph is connected (namely the distance between every two vertices is finite) 2. Consider the longest simple path x0, x1, . ....
Let G = (V, E) be a weighted undirected connected graph that contains a cycle. Let k ∈ E be the edge with maximum weight among all edges in the cycle. Prove that G has a minimum spanning tree NOT including k.
5.40 Show for every connected graph G of diameter 2 or more and every two ver- tices u and v in G that G2 contains a proper u- v path but not necessarily two internally disjoint proper u -v paths.
5.40 Show for every connected graph G of diameter 2 or more and every two ver- tices u and v in G that G2 contains a proper u- v path but not necessarily two internally disjoint proper u -v paths.
Exercise 4 (Aperiodicity of RW on graphs). Let (Xt)tz0 be a random walk on a connected graph G (V,E) (i) Show that all nodes have the same period. (ii) If G contains an odd cycle C (e.g., triangle), show that all nodes in C have period 1. (iii) Show that Xt is aperiodic if and only if G contains an odd cycle. (iv)* (Optional) Show that X, is aperiodic if and only if G is bipartite. (A graph G is...
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....
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...
please show each law for each step when working out the
question. please do not skip and steps and one law per line please
and state every line even if it is the same law please. Show that
¬(?∧(?∨¬¬?))≡¬?
i need to answer like this format. i have tried many times, but
the questions are random.
• You can enter formulas using either the operations 7,1,V, or English words not, and, or. So, the input "p and (q or not...
Please answer only problem 2. Accurate answers with work shown
will receive a 100% rating ASAP. Thank you!
Let G = (V, E) be a graph. We say that a subset S of the vertices V is an independent set if there is no edge in G joining two vertices in S. For example, given a proper colouring of the vertices of G, each colour class (i.e. the set of vertices that have some fixed colour) forms an independent set,...
I have done the a and b, but i'm so confuse with other
questions, could someone help me to fix these questions, thanks so
much.
4 Directed graphs Directed graphs are sometimes used operating systems when trying to avoid deadlock, which is a condition when several processes are waiting for a resource to become available, but this wil never happen because Page 2 p2 T2 Figure 1: Minimal example of a resource allocation graph with deadlock other processes are holding...