Description
1. The dodecahedron graph is depicted below:
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Determine, with justification, whether is Eulerian.
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Show that is Hamiltonian by finding a Hamilton cycle.
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Let be the graph depicted to the right:
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Find a 4-coloring of .
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Show that no 3-coloring of exists.
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3. The graph 3 × 3 is depicted below. Show that this graph is not Hamiltonian. One approach: Show that any Hamilton path must begin and end at even-numbered vertices. Why does this prevent forming a Hamilton cycle?
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Find the chromatic polynomial ( )of = 6 and determine whether − 2 is a factor of ( ).
