7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. Ꮖ (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex x and only intersect C at their final vertices. (b) Show that at least two of Po, P1, P2 have final vertices that are adjacent along C.
7. [10 marks] Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G of length 5. We show how to find a longer cycle in G. Ꮖ (a) Let x be a vertex of G that is not on C. Show that there are three C-paths Po, P1, P2 that are disjoint except at the shared initial vertex x and only intersect C at their final vertices. (b) Show that at least two of Po, P1, P2 have final vertices that are adjacent along C.
Chapter1: Equations, Inequalities, And Mathematical Modeling
Section1.1: Graphs Of Equations
Problem 6ECP: Use symmetry to sketch the graph of xy2=1.
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![7. [10 marks]
Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G
of length 5. We show how to find a longer cycle in G.
Ꮖ
(a) Let x be a vertex of G that is not on C. Show that there are three C-paths
Po, P1, P2 that are disjoint except at the shared initial vertex x and only intersect
C at their final vertices.
(b) Show that at least two of Po, P1, P2 have final vertices that are adjacent along C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3011c556-643e-4a01-b0e0-55d8cf24eddf%2F9c79bd1b-6835-4c3b-8d94-576c54c3b625%2Folzvio8_processed.png&w=3840&q=75)
Transcribed Image Text:7. [10 marks]
Let G = (V,E) be a 3-connected graph with at least 6 vertices. Let C be a cycle in G
of length 5. We show how to find a longer cycle in G.
Ꮖ
(a) Let x be a vertex of G that is not on C. Show that there are three C-paths
Po, P1, P2 that are disjoint except at the shared initial vertex x and only intersect
C at their final vertices.
(b) Show that at least two of Po, P1, P2 have final vertices that are adjacent along C.
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