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At a cupcake stall at the Greenwich market, the owner is selling six different types of cupcakes. The owner sells them in boxes where each box contains exactly two cupcakes, each of different type. Each type of cupcake is used in combination with at least three others. (a) Let G be a graph where each vertex represents one of the cupcakes and where an edge joins two vertices whenever two cupcakes are used in the same box. Let v be an arbitrary vertex in G. What is the smallest degree v can have? Justify your answer. /^ (b) Show that there are three gift boxes which between them have all six types of cupcakes.

At a cupcake stall at the Greenwich market, the owner is selling six different types of cupcakes. The owner sells them in boxes where each box contains exactly two cupcakes, each of different type. Each type of cupcake is used in combination with at least three others. (a) Let G be a graph where each vertex represents one of the cupcakes and where an edge joins two vertices whenever two cupcakes are used in the same box. Let v be an arbitrary vertex in G. What is the smallest degree v can have? Justify your answer. /^ (b) Show that there are three gift boxes which between them have all six types of cupcakes.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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At a cupcake stall at the Greenwich market, the owner is selling six different types of cupcakes. The owner sells them in boxes where each box contains exactly two cupcakes, each of different type. Each type of cupcake is used in combination with at least three others. (a) Let G be a graph where each vertex represents one of the cupcakes and where an edge joins two vertices whenever two cupcakes are used in the same box. Let v be an arbitrary vertex in G. What is the smallest degree v can have? Justify your answer. ' ^ (b) Show that there are three gift boxes which between them have all six types of cupcakes.
Transcribed Image Text:At a cupcake stall at the Greenwich market, the owner is selling six different types of cupcakes. The owner sells them in boxes where each box contains exactly two cupcakes, each of different type. Each type of cupcake is used in combination with at least three others. (a) Let G be a graph where each vertex represents one of the cupcakes and where an edge joins two vertices whenever two cupcakes are used in the same box. Let v be an arbitrary vertex in G. What is the smallest degree v can have? Justify your answer. ' ^ (b) Show that there are three gift boxes which between them have all six types of cupcakes.
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