Question

a. An edge in an undirected connected graph is a bridge if removing it disconnects the...

a.

An edge in an undirected connected graph is a bridge if removing it disconnects the graph. Prove that every connected graph all of whose vertices have even degrees contains no bridges.

b.Let r,s,u be binary relations in U. Verify the following property: if both relations r and s are transitive then the intersection of r and s is transitive too.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that H is a connected graph that contains a proper cycle. Argue that removing any...
Suppose that H is a connected graph that contains a proper cycle. Argue that removing any single edge from this cycle will leave a subgraph of H that remains connected. Make sure you are fully addressing the technical definitions involved --- do not just talk vaguely about vertices being connected, you need to discuss specific paths between vertices.
Suppose that H is a connected graph that contains a proper cycle. Let H′ represent the...
Suppose that H is a connected graph that contains a proper cycle. Let H′ represent the subgraph of H that results by removing a single edge from H, where the edge removed is part of the proper cycle that H contains. Argue that H′ remains connected. Notes. Your argument here needs to be (slightly) different from your argument in Activity 16.3. Make sure you are using the technical definition of connected graph in your argument. What are you assuming about...
(a) Let L be a minimum edge-cut in a connected graph G with at least two...
(a) Let L be a minimum edge-cut in a connected graph G with at least two vertices. Prove that G − L has exactly two components. (b) Let G an eulerian graph. Prove that λ(G) is even.
10.-Construct a connected bipartite graph that is not a tree with vertices Q,R,S,T,U,V,W. What is the...
10.-Construct a connected bipartite graph that is not a tree with vertices Q,R,S,T,U,V,W. What is the edge set? Construct a bipartite graph with vertices Q,R,S,T,U,V,W such that the degree of S is 4. What is the edge set? 12.-Construct a simple graph with vertices F,G,H,I,J that has an Euler trail, the degree of F is 1 and the degree of G is 3. What is the edge set? 13.-Construct a simple graph with vertices L,M,N,O,P,Q that has an Euler circuit...
Let G be a connected simple graph with n vertices and m edges. Prove that G...
Let G be a connected simple graph with n vertices and m edges. Prove that G contains at least m−n+ 1 different subgraphs which are polygons (=circuits). Note: Different polygons can have edges in common. For instance, a square with a diagonal edge has three different polygons (the square and two different triangles) even though every pair of polygons have at least one edge in common.