Question

Managers of a hospital are assigning rooms to patients, each room for a single patient. Patients and rooms are two categories

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Answer #1

The answer should be Bipartite Graph

Ways to prove it:

Use the vertex colouring algorithm:

1) Colour any one of your vertices red.

2) Identify all uncoloured vertices that are adjacent to a red vertex. Colour them yellow.

3) Identify all uncoloured vertices that are adjacent to a yellow vertex. Colour them red.

4) Repeat steps 2 and 3 until all the vertices are coloured red or blue.

5) If there are any two vertices adjacent of the same colour, then your graph is not bipartite, otherwise it is bipartite.

6) If the graph is bipartite, the colouring algorithm will have created the two required sets of points (one red and one yellow).

PATIENTS ROOMS

It is NOT a Complete Bipartite Graph, since edges dont connect each vertex in Rooms to each vertex in Patients.

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