Find a closed walk in a graph that visits every vertex at least once.
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 '18 at 17:58
Pedro SalgadoPedro Salgado
735
add a comment |
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 '18 at 17:58
Pedro SalgadoPedro Salgado
735
add a comment |
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 '18 at 17:58
Pedro SalgadoPedro Salgado
735
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 '18 at 17:58
Pedro SalgadoPedro Salgado
735
asked Nov 22 '18 at 17:58
Pedro SalgadoPedro Salgado
735
asked Nov 22 '18 at 17:58
Pedro SalgadoPedro Salgado
735
asked Nov 22 '18 at 17:58
Pedro SalgadoPedro Salgado
735
asked Nov 22 '18 at 17:58
Pedro SalgadoPedro Salgado
735
735
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 '18 at 18:09
FedericoFederico
4,829514
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1 Answer
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1 Answer
1
active
oldest
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active
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active
oldest
votes
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 '18 at 18:09
FedericoFederico
4,829514
add a comment |
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 '18 at 18:09
FedericoFederico
4,829514
add a comment |
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 '18 at 18:09
FedericoFederico
4,829514
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 '18 at 18:09
FedericoFederico
4,829514
edited Nov 22 '18 at 18:53
answered Nov 22 '18 at 18:09
FedericoFederico
4,829514
answered Nov 22 '18 at 18:09
FedericoFederico
4,829514
answered Nov 22 '18 at 18:09
FedericoFederico
4,829514
4,829514
add a comment |
add a comment |
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