If a graph $G$ has a 2-factor it means it is a 2-regular subgraph that contains all vertices of $G$. Isn't it a hamiltonian cycle? because it is 2-regular so it is a cycle and it contains all vertices of the graph.
2026-03-28 20:56:00.1774731360
Is there a graph with 2-factor that is not hamiltonian?
147 Views Asked by user82004 https://math.techqa.club/user/user82004/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 HAMILTONIAN-PATH
- constraints to the hamiltonian path: can one tell if a path is hamiltonian by looking at it?
- Most efficient way to detect if a series of n edges creates a cycle of size n.
- Is it true that every graph with $n$ vertices in which $\delta(G)\geq\frac{n}{2}-1$ has Hamiltionian path?
- Prove that if a graph $G$ has a Hamilton path then for every $S \subseteq V(G)$ the number of components of $G - S$ is at most $|S| + 1$
- Using Ore's theorem to show the graph contains a Hamilton cycle
- Graph Theory: Hamilton Cycle Definition Clarification
- Does this graph have a Hamiltonian cycle?
- Show the NP completeness of Hamiltonian Path with the knowledge of an directed Euler graph
- Finding Hamiltonian cycle for $N\times M$ grid where $N$ is even
- Graph Theory - Hamiltonian Cycle, Eulerian Trail and Eulerian circuit
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?
A $2$-factor might not be connected; it might consist of multiple cycles that, together, include all the vertices. The standard example is the Petersen graph: