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- In your own words, explain what is required for a trail or circuit to be a Euler trail or circuit.
- Does a Euler trail exist for their graph? Explain specifically using the label and degree of each vertex.
- Does a Euler circuit exist for their graph? Explain specifically using the label and degree of each vertex.
There are 6 people that discussing their favorite foods. Each person will be represented with a letter. A, B, C, D, E, F. Person A, B, and C really like Ice cream. Person D really likes cookies. Person A and C agree that cookies are good. Person D, C, and E like soup quite a bit, and person C, B, and E really like salad. Person B, E, and F all agree that cake is good too. So, person A really likes ice cream and cookies. Person B really likes ice cream, salad, and cake. Person C really likes ice cream, cookies, soup, and salad. Person D really likes cookies and soup. Person E really likes salad and cake. Person F only likes cake. The below graph represents this relationship. Each vertex represents a person, and every edge represents their relationship in similar food preferences to each other. Even if two people share more than one food preference, there will only be one edge connecting them as the edge is just representing that they both like at least one similar food.
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