I wish to show that this graph does not have a Hamiltonian cycle. My thought process has just been to start at arbitrary vertices and to try and find a hamiltonian cycle, which is blunt and inefficient. I need a starting idea or hint to guide me.
2026-03-26 19:08:01.1774552081
Show that this graph has no hamiltonian cycle.
1.9k 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 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?
Notice that the cycles are even. You can redraw the graph as a bipartite graph with uneven parts ($5$ and $6$). This means that every step is between the two parts, and the fact that the two parts do not have the same number of nodes mean that the cycle cannot close - start and end must be on the larger part, which are therefore not connected.
Showing the bipartite nature by colouring: