Questions & Conjectures

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Graph Coloring

From the 2006 ReSEARCH Group

Questions/Conjectures from ReSEARCH Session 11:

Conjectures made that are related to Scheduling Problem 1:

Conjecture 1: If you add a new person to any one tour list, it wouldn’t affect our schedule. (Alicia C. & Aviva S.)

Conjecture 2: If a new person is added to any two tour lists, then you might have to rearrange your schedule. (Alicia C. & Aviva S.)

Conjecture 3: When a new person signs up for the pool and math museum, there have to be four tour times. (Alicia C. & Aviva S.)

Conjecture 4: The schedule wouldn’t change if you signed up three tours that were already placed at different times. (Alicia L. & Jane L.)

Conjecture 5: Only people scheduled for two or more tours are not negligible for determining schedules. (Alicia L. & Jane L.) Furthermore, those signed up for only one tour can go throw themselves off a cliff. (J.K.)

Conjecture 6: It is possible for there to be seven activities (tours) offered in the three time periods. (Yasemin O. & Lisa M.)

Question 1: If you changed just one person on the tour could you make the schedule impossible to make? (Shelby H.)

Question 2: If you cancel out Food Court and Gymnasium, what possible tours can you make? (Lisa M.)