Question

(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.

Homework Answers

Answer #2

answered by: anonymous
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
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.
Exercise 10.5.4: Edge connectivity between two vertices. Two vertices v and w in a graph G...
Exercise 10.5.4: Edge connectivity between two vertices. Two vertices v and w in a graph G are said to be 2-edge-connected if the removal of any edge in the graph leaves v and w in the same connected component. (a) Prove that G is 2-edge-connected if every pair of vertices in G are 2-edge-connected.
Prove that if G is a connected graph with exactly 4 vertices of odd degree, there...
Prove that if G is a connected graph with exactly 4 vertices of odd degree, there exist two trails in G such that each edge is in exactly one trail. Find a graph with 4 vertices of odd degree that’s not connected for which this isn’t true.
let G be a connected graph such that the graph formed by removing vertex x from...
let G be a connected graph such that the graph formed by removing vertex x from G is disconnected for all but exactly 2 vertices of G. Prove that G must be a path.
I.15: If G is a simple graph with at least two vertices, prove that G has...
I.15: If G is a simple graph with at least two vertices, prove that G has two vertices of the same degree.    Hint: Let G have n vertices. What are possible different degree values? Different values if G is connected?
a) Let k>1 be the size of a minimum edge cut in G. Show that the...
a) Let k>1 be the size of a minimum edge cut in G. Show that the deletion of k edges from G results in at most 2 components. b) Is the same true for vertex cuts? Justify your answer.
Let G be a simple graph having at least one edge, and let L(G) be its...
Let G be a simple graph having at least one edge, and let L(G) be its line graph. (a) Show that χ0(G) = χ(L(G)). (b) Assume that the highest vertex degree in G is 3. Using the above, show Vizing’s Theorem for G. You may use any theorem from class involving the chromatic number, but no theorem involving the chromatic index
Let G be a simple graph with at least two vertices. Prove that there are two...
Let G be a simple graph with at least two vertices. Prove that there are two distinct vertices x, y of G such that deg(x)= deg(y).
Let e be the unique lightest edge in a graph G. Let T be a spanning...
Let e be the unique lightest edge in a graph G. Let T be a spanning tree of G such that e ∉ T . Prove using elementary properties of spanning trees (i.e. not the cut property) that T is not a minimum spanning tree of G.
GRAPH THEORY: Let G be a graph which can be decomposed into Hamilton cycles. Prove that...
GRAPH THEORY: Let G be a graph which can be decomposed into Hamilton cycles. Prove that G must be k-regular, and that k must be even. Prove that if G has an even number of vertices, then the edge chromatic number of G is Δ(G)=k.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT