What is the first line of the backwards direction of this proof? 1.Assume G is a block. 2.Assume every pair of vertices lie on a common cycle. 3.Assume.

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Presentation transcript:

What is the first line of the backwards direction of this proof? 1.Assume G is a block. 2.Assume every pair of vertices lie on a common cycle. 3.Assume G is not a block. 4.Assume there exists a pair of vertices that do not lie on a common cycle. 5.Assume every block has a common cycle. 6.Assume every cycle is a block.

What is the next line of the proof, given that we will do a proof by contradiction? 1.Assume G is a block. 2.Assume every pair of vertices lie on a common cycle. 3.Assume G is not a block. 4.Assume there exists a pair of vertices that do not lie on a common cycle. 5.Assume every block has a common cycle. 6.Assume every cycle is a block.

Is it possible to find an Euler Circuit in this graph: 1). Yes 2). No 3). I have absolutely no idea

Is it possible to find an Euler Circuit in this graph: 1). Yes 2). No 3). I have absolutely no idea

a b c d e f g h j i k m l p o n Is it possible to find an Euler Circuit is this graph? 1). Yes 2). No 3). I have absolutely no idea.

What is the first line of the proof? 1). Assume G has an Eulerian circuit. 2). Assume every vertex has even degree. 3). Let v be any vertex in G. 4). Let v be a vertex of odd degree.

What is the second line of the proof? 1). Assume G has an Eulerian circuit. 2). Assume every vertex has even degree. 3). Let v be any vertex in G. 4). Let v be a vertex of odd degree.

Can this figure be drawn without lifting your pencil from the paper? 1). Yes, start anywhere 2). Yes, but there are restrictions on where you start. 3). No 4). I have absolutely no idea.

Can this figure be drawn without lifting your pencil from the paper? 1). Yes, start anywhere 2). Yes, but there are restrictions on where you start. 3). No 4). I have absolutely no idea.

Can this figure be drawn without lifting your pencil from the paper? 1). Yes, start anywhere 2). Yes, but there are restrictions on where you start. 3). No 4). I have absolutely no idea.

Can this figure be drawn without lifting your pencil from the paper? 1). Yes, start anywhere 2). Yes, but there are restrictions on where you start. 3). No 4). I have absolutely no idea.

Can this figure be drawn without lifting your pencil from the paper? 1). Yes, start anywhere 2). Yes, but there are restrictions on where you start. 3). No 4). I have absolutely no idea.