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6.8

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Topic 6 - Discrete mathematics » 6.8

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Directly related questions

18M.2.hl.TZ0.3c.ii: Explain the consequences of having a Hamiltonian cycle for Pauline’s visit to the ground floor of...
18M.2.hl.TZ0.3c.i: Write down a Hamiltonian cycle for the graph G.
18M.2.hl.TZ0.3b.ii: Explain the consequences of having an Eulerian trail but not an Eulerian circuit, for Pauline’s...
18M.2.hl.TZ0.3b.i: Explain why the graph G has an Eulerian trail but not an Eulerian circuit.
16M.2.hl.TZ0.1b: Determine whether or not the graph is Hamiltonian.
16M.2.hl.TZ0.1a: Determine whether or not the graph is Eulerian.
17M.2.hl.TZ0.1b: Use Dijkstra’s algorithm to find the path of minimum total weight joining A to D, stating this...
17M.2.hl.TZ0.1a.ii: Write down an Eulerian trail.
17M.2.hl.TZ0.1a.i: State what features of the graph enable you to state that \(G\) contains an Eulerian trail but no...
17M.1.hl.TZ0.11c.i: Explain why a graph containing a cycle of length three cannot be bipartite.
15M.1.hl.TZ0.4c: Show that \(G\) has a Hamiltonian cycle.
15M.1.hl.TZ0.4b: Explain why \(G\) does not contain an Eulerian circuit.
11M.2.hl.TZ0.1d: State with reasons whether or not this graph has (i) an Eulerian circuit; (ii) an...
11M.2.hl.TZ0.1e: Find the number of walks of length \(4\) from E to F.
10M.2.hl.TZ0.3a: (i) Explain briefly what features of the graph enable you to state that \(G\) has an Eulerian...
13M.2.hl.TZ0.4b: Determine, giving reasons, whether \(H\) has (i) a Hamiltonian path; (ii) a...
12M.2.hl.TZ0.2A.b: (i) Explain what feature of \(H\) guarantees that it has an Eulerian circuit. (ii) Write...
12M.2.hl.TZ0.2A.c: (i) Find the number of different walks of length five joining A to B. (ii) Determine how...

Sub sections and their related questions

Walks, trails, paths, circuits, cycles.

11M.2.hl.TZ0.1d: State with reasons whether or not this graph has (i) an Eulerian circuit; (ii) an...
11M.2.hl.TZ0.1e: Find the number of walks of length \(4\) from E to F.
10M.2.hl.TZ0.3a: (i) Explain briefly what features of the graph enable you to state that \(G\) has an Eulerian...
13M.2.hl.TZ0.4b: Determine, giving reasons, whether \(H\) has (i) a Hamiltonian path; (ii) a...
12M.2.hl.TZ0.2A.b: (i) Explain what feature of \(H\) guarantees that it has an Eulerian circuit. (ii) Write...
12M.2.hl.TZ0.2A.c: (i) Find the number of different walks of length five joining A to B. (ii) Determine how...
16M.2.hl.TZ0.1a: Determine whether or not the graph is Eulerian.
16M.2.hl.TZ0.1b: Determine whether or not the graph is Hamiltonian.
18M.2.hl.TZ0.3b.i: Explain why the graph G has an Eulerian trail but not an Eulerian circuit.
18M.2.hl.TZ0.3b.ii: Explain the consequences of having an Eulerian trail but not an Eulerian circuit, for Pauline’s...
18M.2.hl.TZ0.3c.i: Write down a Hamiltonian cycle for the graph G.
18M.2.hl.TZ0.3c.ii: Explain the consequences of having a Hamiltonian cycle for Pauline’s visit to the ground floor of...

Eulerian trails and circuits.

13M.2.hl.TZ0.4b: Determine, giving reasons, whether \(H\) has (i) a Hamiltonian path; (ii) a...
15M.1.hl.TZ0.4b: Explain why \(G\) does not contain an Eulerian circuit.
18M.2.hl.TZ0.3b.i: Explain why the graph G has an Eulerian trail but not an Eulerian circuit.
18M.2.hl.TZ0.3b.ii: Explain the consequences of having an Eulerian trail but not an Eulerian circuit, for Pauline’s...
18M.2.hl.TZ0.3c.i: Write down a Hamiltonian cycle for the graph G.
18M.2.hl.TZ0.3c.ii: Explain the consequences of having a Hamiltonian cycle for Pauline’s visit to the ground floor of...

Hamiltonian paths and cycles.

13M.2.hl.TZ0.4b: Determine, giving reasons, whether \(H\) has (i) a Hamiltonian path; (ii) a...
15M.1.hl.TZ0.4c: Show that \(G\) has a Hamiltonian cycle.
18M.2.hl.TZ0.3b.i: Explain why the graph G has an Eulerian trail but not an Eulerian circuit.
18M.2.hl.TZ0.3b.ii: Explain the consequences of having an Eulerian trail but not an Eulerian circuit, for Pauline’s...
18M.2.hl.TZ0.3c.i: Write down a Hamiltonian cycle for the graph G.
18M.2.hl.TZ0.3c.ii: Explain the consequences of having a Hamiltonian cycle for Pauline’s visit to the ground floor of...