Question

A graph is called planar if it can be
drawn in the plane without any edges crossing. The Euler’s formula
states that *v* − *e* + *r* = 2*,*
where *v,e,* and *r* are the numbers of vertices,
edges, and regions in a planar graph, respectively. For the
following problems, let *G* be a planar simple graph with 8
vertices.

- Find the maximum number of edges in
*G*. - Find the maximum number of edges in
*G,*if*G*has no circuits of length 3.

Answer #1

30. a) Show if G is a connected planar simple graph with v
vertices and e edges with v ≥ 3 then e ≤ 3v−6.
b) Further show if G has no circuits of length 3 then e ≤
2v−4.

Q. a graph is called k-planar if every vertex has degree
k.
(a) Explain why any k-regular graph with 11 vertices should contain
an Euler’s circuit.
(what are the possible values of k).
(b) Suppose G is a 6-regular graph. Must the chromatic number of G
be at leat 6? Explain.

1. What is an ISP (Integrated Service Provider) for supply
chains? (1 point)
A. A consultant agency which integrates the supply chain for
companies
B. A 2 PL or a 3PL, but not a 4PL
C. A company supplying transportation and warehousing
services
D. A logistics service company specialized in suppling VAS (value
added
services)
2. What characterizes a 4 PL? (1 point)
A. They are non-asset based and provides integrated services
primarily
supplied by asset based providers, for example...

Please answer the following Case
analysis questions
1-How is New Balance performing compared to its primary rivals?
How will the acquisition of Reebok by Adidas impact the structure
of the athletic shoe industry? Is this likely to be favorable or
unfavorable for New Balance?
2- What issues does New Balance management need to address?
3-What recommendations would you make to New Balance Management?
What does New Balance need to do to continue to be successful?
Should management continue to invest...

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