Find a closed walk in a graph that visits every vertex at least once.
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Prove that, for all finite connected graph, it is possible to find a closed walk that visits every vertex of the graph at least once.
I have no idea. I've try to prove using minimum spanning tree, but I need a closed walk. Any idea?
graph-theory
asked Nov 22 at 17:58
Pedro Salgado
675
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up vote
0
down vote
favorite
Prove that, for all finite connected graph, it is possible to find a closed walk that visits every vertex of the graph at least once.
I have no idea. I've try to prove using minimum spanning tree, but I need a closed walk. Any idea?
graph-theory
asked Nov 22 at 17:58
Pedro Salgado
675
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Prove that, for all finite connected graph, it is possible to find a closed walk that visits every vertex of the graph at least once.
I have no idea. I've try to prove using minimum spanning tree, but I need a closed walk. Any idea?
graph-theory
asked Nov 22 at 17:58
Pedro Salgado
675
Prove that, for all finite connected graph, it is possible to find a closed walk that visits every vertex of the graph at least once.
I have no idea. I've try to prove using minimum spanning tree, but I need a closed walk. Any idea?
graph-theory
graph-theory
asked Nov 22 at 17:58
Pedro Salgado
675
asked Nov 22 at 17:58
Pedro Salgado
675
asked Nov 22 at 17:58
Pedro Salgado
675
asked Nov 22 at 17:58
Pedro Salgado
675
asked Nov 22 at 17:58
Pedro Salgado
675
675
add a comment |
add a comment |
1 Answer
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Enumerate you vertices $v_1,dots,v_n$. Because $G$ is connected, you can find a path from $v_i$ to $v_{i+1}$ for every $i=1,dots,n-1$. So you construct a path starting at $v_1$, visiting $v_2$, $v_3$, etc., and ending at $v_n$. Now you just go back to $v_1$ to close your tourist tour of the graph.
answered Nov 22 at 18:09
Federico
4,238512
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1 Answer
1
active
oldest
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
accepted
Enumerate you vertices $v_1,dots,v_n$. Because $G$ is connected, you can find a path from $v_i$ to $v_{i+1}$ for every $i=1,dots,n-1$. So you construct a path starting at $v_1$, visiting $v_2$, $v_3$, etc., and ending at $v_n$. Now you just go back to $v_1$ to close your tourist tour of the graph.
answered Nov 22 at 18:09
Federico
4,238512
add a comment |
up vote
1
down vote
accepted
Enumerate you vertices $v_1,dots,v_n$. Because $G$ is connected, you can find a path from $v_i$ to $v_{i+1}$ for every $i=1,dots,n-1$. So you construct a path starting at $v_1$, visiting $v_2$, $v_3$, etc., and ending at $v_n$. Now you just go back to $v_1$ to close your tourist tour of the graph.
answered Nov 22 at 18:09
Federico
4,238512
add a comment |
up vote
1
down vote
accepted
up vote
1
down vote
accepted
Enumerate you vertices $v_1,dots,v_n$. Because $G$ is connected, you can find a path from $v_i$ to $v_{i+1}$ for every $i=1,dots,n-1$. So you construct a path starting at $v_1$, visiting $v_2$, $v_3$, etc., and ending at $v_n$. Now you just go back to $v_1$ to close your tourist tour of the graph.
answered Nov 22 at 18:09
Federico
4,238512
Enumerate you vertices $v_1,dots,v_n$. Because $G$ is connected, you can find a path from $v_i$ to $v_{i+1}$ for every $i=1,dots,n-1$. So you construct a path starting at $v_1$, visiting $v_2$, $v_3$, etc., and ending at $v_n$. Now you just go back to $v_1$ to close your tourist tour of the graph.
answered Nov 22 at 18:09
Federico
4,238512
edited Nov 22 at 18:53
answered Nov 22 at 18:09
Federico
4,238512
answered Nov 22 at 18:09
Federico
4,238512
answered Nov 22 at 18:09
Federico
4,238512
4,238512
add a comment |
add a comment |
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