Question: If G is a connected planar graph with all circuits of length at least k, show that the inequality e 3v 6 can be strengthened

If G is a connected planar graph with all circuits of length at least k, show that theinequality e 3v 6 can be strengthened to e [k/(k2)](v 2). (Hint: The degreeof a region will be at least k.)

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

search the text name on the Google for book Show written solutions for all of the following problems. Unit 7: Graph Theory Text: Discrete Mathematics: An Open Introduction, 3"I Edition. 4.1...

(a) Let k Z+, k ¥ 3. If G = (V, E) is a connected planar graph with |V| = v, |E| = e, and each cycle of length at least k, prove that (b) What is the minimal cycle length in K3,3? (c) Use parts...

1 . ( a ) For a graph G , consider two edge - weight functions w 1 and w 2 such that w 1 ( e ) w 1 ( e ) w 2 ( e ) w 2 ( e ) for all edges e , e E . Show that T is an MST wrt w 1 iff it is an MST wrt...

You$must$attach$this$cover$page$to$the$front$of$your$HW$or$you$will$lose$5$points.$ $ $ APMA$1860$Homework$2$ $ $ First$Name:$____________________________$$$Last$Name:$______________________________$...

(a) (b) (C) Show that a connected graph with at least as many edges as vertices must contain a cycle. Let G be a connected graph with n vertices and m edges for n 2 2. Show that G contains a...

Let r and s be solutions to the quadratic equation x 2 b x + c = 0. For n N, define d0 = 0 d1 = r s dn = b dn1 c dn2 (n 2) Prove that dn = r n s n for all n N. [4 marks] (b) Recall that a commutative...

Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

answer the question clearly You are building a flight-control system for which a convincing safety case must be made. Would you assign the tasks of safety requirements engineering, test case...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

Entity A is a local construction company, which provides construction services to different types of customers. On 16 December 2017, Entity A ordered a concrete plant from Entity B. The listed price...

If the individual subsidiary ledger accounts contained the following data: Cadence Company, Vendor, $169, credit balance Franklin Enterprises, Customer, $404, debit balance Marcelo Construction,...

This capital budgeting method ignores future cash flows and the time value of money. 0 2 2 * 3 3 Multiple Choice AAR Payback Proftability Index IRR NPV

REVISED CORPORATION LAW 1.) Rules of action adopted by a corporation for its internal regulation: * A.) Primary franchise B.) Secondary franchise C.) Articles of Incorporation D.) By-laws E.) Charter...