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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.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.2: Graphs Of Equations In Two Variables; Circles
Problem 5E: a If a graph is symmetric with respect to the x-axis and (a,b) is on the graph, then (,) is also on...
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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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