Question 3.109

79. The owner of a new pet store wishes to display tropical fish in display tanks. The accompanying table shows the incompatibilities between the species, in the sense that an X indicates that it is unwise to allow those species in the row and column that meet at the X to be in the same tank.

X X X
X X
X X X
X X X
X X X
X X X X
X X X X X
X X X X
X X X
  1. Draw an appropriate graph to represent the information in the table.
  2. What is the minimum number of tanks needed to display all the fish she wishes to sell?
  3. Display the species so that the number of species in each tank is as nearly equal as possible.

79.

(a) Drawings can vary. Possible renderings include the following:

image

(b) 4

(c) The coloring in part (a) indicates one possible arrangement.