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2. Eulerian and Hamiltonian tours (a) State Ore's Theorem (that ensures a graph is Hamiltonian) (b) Explain why the graph K2,3 fails to meet the criteria for Ore's theorem (c) Explain why K2,3 doesn't have a Hamiltonian circuit (Question 2 continued) (d) For this question, use the diagram below (Figure: 2) g h a b Figure 2: A graph C i. Check that the graph satisfies Eulers criterion. ii. Use Fleury's algorithm (avoiding bridges) to find an Eulerian tour, making sure to • Start at g and go to i (g → i) • When given a choice, always choose the one that appears first alphabetically (e.g. choose b over c or e.) • Indicate any bridges, either taken or avoided iii. Use Hierholzer's algorithm (stiching together cycles) to find an Eulerian circuit, mak- ing sure to • Use these cycles in the given order P₁ = gic C1 = fedcbhgf C3 = abiegja

2. Eulerian and Hamiltonian tours (a) State Ore's Theorem (that ensures a graph is Hamiltonian) (b) Explain why the graph K2,3 fails to meet the criteria for Ore's theorem (c) Explain why K2,3 doesn't have a Hamiltonian circuit (Question 2 continued) (d) For this question, use the diagram below (Figure: 2) g h a b Figure 2: A graph C i. Check that the graph satisfies Eulers criterion. ii. Use Fleury's algorithm (avoiding bridges) to find an Eulerian tour, making sure to • Start at g and go to i (g → i) • When given a choice, always choose the one that appears first alphabetically (e.g. choose b over c or e.) • Indicate any bridges, either taken or avoided iii. Use Hierholzer's algorithm (stiching together cycles) to find an Eulerian circuit, mak- ing sure to • Use these cycles in the given order P₁ = gic C1 = fedcbhgf C3 = abiegja

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. Eulerian and Hamiltonian tours (a) State Ore's Theorem (that ensures a graph is Hamiltonian) (b) Explain why the graph K2,3 fails to meet the criteria for Ore's theorem (c) Explain why K2,3 doesn't have a Hamiltonian circuit (Question 2 continued) (d) For this question, use the diagram below (Figure: 2) g h a b Figure 2: A graph C i. Check that the graph satisfies Eulers criterion. ii. Use Fleury's algorithm (avoiding bridges) to find an Eulerian tour, making sure to • Start at g and go to i (g → i) • When given a choice, always choose the one that appears first alphabetically (e.g. choose b over c or e.) • Indicate any bridges, either taken or avoided iii. Use Hierholzer's algorithm (stiching together cycles) to find an Eulerian circuit, mak- ing sure to • Use these cycles in the given order P₁ = gic C1 = fedcbhgf C3 = abiegja
Transcribed Image Text:2. Eulerian and Hamiltonian tours (a) State Ore's Theorem (that ensures a graph is Hamiltonian) (b) Explain why the graph K2,3 fails to meet the criteria for Ore's theorem (c) Explain why K2,3 doesn't have a Hamiltonian circuit (Question 2 continued) (d) For this question, use the diagram below (Figure: 2) g h a b Figure 2: A graph C i. Check that the graph satisfies Eulers criterion. ii. Use Fleury's algorithm (avoiding bridges) to find an Eulerian tour, making sure to • Start at g and go to i (g → i) • When given a choice, always choose the one that appears first alphabetically (e.g. choose b over c or e.) • Indicate any bridges, either taken or avoided iii. Use Hierholzer's algorithm (stiching together cycles) to find an Eulerian circuit, mak- ing sure to • Use these cycles in the given order P₁ = gic C1 = fedcbhgf C3 = abiegja
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