All Questions
Tagged with eulerian-path bipartite-graphs
14
questions
0
votes
1
answer
195
views
Why is a bipartite graph in which every vertex has degree exactly $2$ is simply a cycle?
I am trying to intuitively understand why a bipartite graph in which every vertex has degree exactly $2$ is simply a cycle. So far, I have tried to intuitively justify this by saying that an Eulerian ...
- 3,019
0
votes
1
answer
57
views
Are the following two properties of Eulerian graphs true?
Can someone help to verify the following two properties, perhaps by indicating what properties of eulerian graphs is used in them?
Q1: Let $G$ be a connected graph containing a Eulerian circuit. If $G$...
- 183
2
votes
1
answer
150
views
Every bipartite Eulerian graph is a Hamilton graph
This is a true/false question I'm trying to solve to prepare for my exam. Could someone confirm my answer and help me prove it?
What I think: false, but I can not come up with an example.
- 115
0
votes
1
answer
98
views
Simple connected eulerian graph $G = (V, E)$ cannot be bipartite if $(V, E - \{e_1,e_2,e_3\})$ is also eulerian
Let $G = (V, E)$ be a simple connected eulerian graph, I was asked to prove that it cannot be bipartite if $(V, E - \{ e_1,e_2,e_3 \})$ is also eulerian.
While processing my proof I came up with this ...
- 123
0
votes
2
answers
456
views
Bipartite Connected Graph, Eulerian Circuit
Give an example of a bipartite connected graph which has an even number of vertices and an Eulerian circuit, but does not have a perfect matching.
- 29
0
votes
1
answer
447
views
Graph which is Bipartite, has an Euler circuit, but not a Hamiltonian circuit
Is there a graph which is bipartite, has an Euler circuit, but not a Hamiltonian circuit?
I know the answer is yes, but if you consider something like this:
I don't think this would be bipartite, ...
- 35
1
vote
1
answer
4k
views
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
1
vote
1
answer
593
views
Difference between chromatic number and minimal vertex covering
I have just started learning graph theory not long ago, this is a past year problem and I got the correct answer by chance(True/False questions), wanted to check my understanding on this site.
My ...
1
vote
0
answers
438
views
What is connection between Euler graphs, bipartite graphs and having even number of vertices?
Prove or disprove:
If $G$ is an Euler graph with even number of vertices then it's bipartite.
If $G$ is an Euler and bipartite graph then the number of its vertices is even.
The second claim is ...
- 611
1
vote
1
answer
576
views
Question on degree sequence of eulerian, hamiltonian bipartite graph
I've gathered that it requires a cycle with degree 10 to be considered hamiltonian and it is bipartite so there can not be any odd cycle, lastly it is eulerian hence every edge set can be partitioned ...
- 11
1
vote
2
answers
7k
views
How can a bipartite graph be Eulerian?
From the way I understand it:
(1) a trail is Eulerian if it contains every edge exactly once.
(2) a graph has a closed Eulerian trail iff it is connected and every vertex has even degree
(3) a ...
- 11
1
vote
1
answer
189
views
Determine if G is bipartite. Find a maximal path and Eulerian circuit in G.
Would I be correct to assume that a maximal path would be e-c-a-b-h-d-f-g?
Is this my eulerian circuit: c-e-b-a-c-h-b-d-f-g-d-h-f-c?
Also, am I right to say it is not bipartite because it contains an ...
0
votes
1
answer
1k
views
Bipartite graph. average degree. Euler circuit. [closed]
This is such a hard question to get my head around. Can anyone help solve this?
- 287
1
vote
0
answers
123
views
Eulerian Cycle in a Random Bipartite Graph
I want to know (or possibly a pointer to a relevant text) the probability of having an Eulerian cycle in a random bipartite graph. I assume an Erdos-Renyi model $G(n,m,p)$, where the number of nodes ...
