Is there a "generalized" Ramsey theory? How large must a graph be such that, with arbitrary connections between vertices, the existence of arbitrarily defined subgraphs is assured?
2026-03-28 12:12:42.1774699962
Ramsey theory, generalized
81 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 RAMSEY-THEORY
- Name of Theorem for Coloring of $\{1, \dots, n\}$
- Probability that in fully connected graph there is a clique of different colors
- Ramsey Number Upper Bound
- Ramsey Numbers with 3 Variables
- Van der Waerden type theorem
- Colouring of a grid $\mathbb{Z}^2$.
- Has this Ramsey-type function been studied?
- 2-coloring of R(m,m) with no monochromatic $K_m$
- Ramsey's Theorem(Numerical Example)
- Tic-tac-toe game on the cube 3×3×3
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?
The paper below rigorously states in the abstract a generalization of Ramsey's Theorem for finding monochromatic subgraphs (not necessarily subcliques/complete graphs) when coloring some arbitrary initial graph.
http://math.mit.edu/~fox/paper-Ramseymultiplecolors.pdf
This seems like a difficult question and a difficult area of research and I don't currently know of any other papers on this topic. I expect that any arbitrary starting graph (a graph with 'arbitrary connections between the vertices') is too wild to study and obtain any reasonable results. I expect that some conditions such as bipartite, postive density of edges, or regularity will be needed in order to make any reasonable progress on the type of question that you are interested in.