All Questions
Tagged with eulerian-path solution-verification
8
questions
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Are there at least $|V|$ Eulerian tours in $G$ if $G$ is even degree and connected? (My proof)
I believe there to be at least $|V|$ Eulerian tours in $G$ if $G$ is even degree and connected, and want to confirm that my reasoning of this is sound. (I am using the definition of Eulerian tour to ...
- 3,019
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1
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566
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Is a cycle for a graph containing all edges of the graph necessarily an Euler cycle?
Under the definition that an Euler cycle is a cycle passing every edge in G only once, and finishing on the same vertex it begins on.
I have reasoned that the answer to this would be no, since it ...
- 65
1
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When does the complete bipartite graph K n,m have an Euler Trail(Path)?
So I know that an Euler trail must have no more than two odd degree vertices.
So does this mean that either $n$ or $m$ must be odd? Or is it $n = m + 1$?
- 147
2
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Is it possible that exactly one of $G$ and $H$ has an Euler trail, if both graphs are homeomorphic?
Let $G$ and $H$ be loop-free homeomorphic undirected graphs with no
isolated vertices. Is it possible that exactly one of $G$ and $H$ has
an Euler trail?
My approach is that if graph $G$ has an ...
- 321
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1
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105
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Question on graph Connectivity.
Question
Consider the statement below-:
$\text{1.In simple graph with 6 vertices,if degree of each vertex is 2 ,then graph is connected}$
$\text{2.In simple graph with 6 vertices,if degree of each ...
- 2,540
1
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1
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Prove: Let $T$ be a tree, show that each Hamiltonian path is also Eulerian
I want to be sure if my proof is correct.
Let's assume that in $T$ (tree graph) there is an Hamiltonian path. Show that the path is also Eulerian.
Let's look on the subgraph of the Hamiltonian path. ...
- 15
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621
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Any Eulerian trail which is not an Eulerian circuit must start and end at an odd vertex.
Theorem Any Eulerian trail which is not an Eulerian circuit must start and end at an odd vertex.
https://proofwiki.org/wiki/Characteristics_of_Traversable_Graph
Proof:
Let G be a graph.
...
user420360
4
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Graph $G$ has k vertices of odd degree, prove there is $\dfrac{k}{2}$ non-closed trails that cover all the edges of the graph exactly once.
A graph $G$ has k vertices of odd degree, prove that there is $\dfrac{k}{2}$ non-closed trails on the graph that cover all the edges of the graph exactly once.
Here is my proof:
The graph has $k$ ...
- 1,535