Orion was a great warrior of ancient Greece. He was so important that Zeus created a constellation illustrating him in a fight position. Consider the graph in the image below, modeling the constellation with 15 nodes (the stars) and 16 links, without self-loops. Based on the statements below, choose the correct alternative.
(I) If Orion's belt is removed (the three nodes near the middle of the image), the resulting graph is bipartite.
(II) For any adjacency matrix for this graph, the sum of the values in the secondary diagonal is greater than or equal to the sum in the main diagonal.
(III) Removing Orion's shield (the six rightmost nodes), the resulting graph is Hamiltonian.
(IV) Removing Orion's belt and shield, the resulting graph is Eulerian.
- Only II is correct
- II and III are correct
- I and IV are correct
- All of the alternatives are correct
- None of the above
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