The rules for an Euler path is:
A graph will contain an Euler path if it contains at most two vertices of odd degree.
My graphs are undirected and connected and fulfill the above condition.
Yet these two graphs have no Eulerian path. Why is it so?
2026-03-26 20:25:48.1774556748
Connected graph with two vertices of odd degrees, not containing an Euler path?
918 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in GRAPH-THEORY
- characterisation of $2$-connected graphs with no even cycles
- Explanation for the static degree sort algorithm of Deo et al.
- A certain partition of 28
- decomposing a graph in connected components
- Is it true that if a graph is bipartite iff it is class 1 (edge-coloring)?
- Fake induction, can't find flaw, every graph with zero edges is connected
- Triangle-free graph where every pair of nonadjacent vertices has exactly two common neighbors
- Inequality on degrees implies perfect matching
- Proving that no two teams in a tournament win same number of games
- Proving that we can divide a graph to two graphs which induced subgraph is connected on vertices of each one
Related Questions in EULERIAN-PATH
- Proof for a graph has Euler tour iff each vertex has even degree
- Graph Theory: Euler Trail and Euler Graph
- Determine if G is bipartite. Find a maximal path and Eulerian circuit in G.
- Proving the graph $V=\{S\subset\{1,2\ldots9\}\mid3\leq\left|S\right|\leq4\},\,\,\,E=\{(u,v)\mid u\subset v\}$ is connected
- Graph Theory - Hamiltonian Cycle, Eulerian Trail and Eulerian circuit
- How can a bipartite graph be Eulerian?
- How to find Eulerian path in the given graph?
- Question on degree sequence of eulerian, hamiltonian bipartite graph
- Sufficient condition for graph isomorphism assuming same degree sequence
- Non isomorphic graphs with closed eulerian chains
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?
These graphs do not have Eulerian paths because they have more than two vertices of odd degree. In this case, both have four vertices of odd degree, which is more than 2.
I have gone through and circled and labeled all of the vertices with odd degree so you can check over which vertices you may have missed.