h5 - G be Hamiltonian if | E | = 17? You need to justify...

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MATH 4171 Graph Theory SPRING 2006 Homework Set V (4 problems) Due date : Monday 4-3-06 1. Theorem 4.8 states that a necessary condition for a graph G = ( V,E ) to be Hamiltonian is that G - S has at most | S | components, for all S V . Is this condition suFcient? In other words, must G = ( V,E ) be Hamiltonian if G - S has at most | S | components, for all S V ? You need to justify your conclusion. 2. Let G = ( V,E ) be a simple graph on 7 vertices. (a) Must G be Hamiltonian if | E | = 16? (b) Must
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Unformatted text preview: G be Hamiltonian if | E | = 17? You need to justify your conclusions. 3. Prove or disprove: every directed edge in a strongly connected tournament is contained in a directed Hamiltonian cycle. 4. ind all 4-regular maximal planar graphs (the following graph, known as the octahedron is such a graph). You need to justify your conclusion. Important No Late Homework Will be Accepted...
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