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Idle Miner Tycoon Cheats Generator 2024 Free No Verification (New.updated) ★★

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Idle Miner Tycoon Cheats Generator 2024 Free No Verification (New.updated)

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Even vs. odd latin squares ★★★

Author(s): Alon; Tarsi

A latin square is even if the product of the signs of all of the row and column permutations is 1 and is odd otherwise.

Conjecture   For every positive even integer $ n $, the number of even latin squares of order $ n $ and the number of odd latin squares of order $ n $ are different.

Keywords: latin square

Every 4-connected toroidal graph has a Hamilton cycle ★★

Author(s): Grunbaum; Nash-Williams

Conjecture   Every 4-connected toroidal graph has a Hamilton cycle.

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S(S(f)) = S(f) for reloids ★★

Author(s): Porton

Question   $ S(S(f)) = S(f) $ for every endo-reloid $ f $?

Keywords: reloid

Chowla's cosine problem ★★★

Author(s): Chowla

Problem   Let $ A \subseteq {\mathbb N} $ be a set of $ n $ positive integers and set \[m(A) = - \min_x \sum_{a \in A} \cos(ax).\] What is $ m(n) = \min_A m(A) $?

Keywords: circle; cosine polynomial

Golf Battle Cheats Generator (Ios Android) ★★

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Golf Battle Cheats Generator (Ios Android)

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Toon Blast Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra) ★★

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Toon Blast Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra)

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eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (FREE METHOD) ★★

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eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (FREE METHOD)

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Legal Bleach Brave Souls Cheats Generator No Human Verification 2024 (No Surveys Needed) ★★

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Legal Bleach Brave Souls Cheats Generator No Human Verification 2024 (No Surveys Needed)

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"Working Cheats" Apex Legends Coins Generator Ios Android 2024 ★★

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"Working Cheats" Apex Legends Coins Generator Ios Android 2024

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Vertex Coloring of graph fractional powers ★★★

Author(s): Iradmusa

Conjecture   Let $ G $ be a graph and $ k $ be a positive integer. The $ k- $power of $ G $, denoted by $ G^k $, is defined on the vertex set $ V(G) $, by connecting any two distinct vertices $ x $ and $ y $ with distance at most $ k $. In other words, $ E(G^k)=\{xy:1\leq d_G(x,y)\leq k\} $. Also $ k- $subdivision of $ G $, denoted by $ G^\frac{1}{k} $, is constructed by replacing each edge $ ij $ of $ G $ with a path of length $ k $. Note that for $ k=1 $, we have $ G^\frac{1}{1}=G^1=G $.
Now we can define the fractional power of a graph as follows:
Let $ G $ be a graph and $ m,n\in \mathbb{N} $. The graph $ G^{\frac{m}{n}} $ is defined by the $ m- $power of the $ n- $subdivision of $ G $. In other words $ G^{\frac{m}{n}}\isdef (G^{\frac{1}{n}})^m $.
Conjecture. Let $ G $ be a connected graph with $ \Delta(G)\geq3 $ and $ m $ be a positive integer greater than 1. Then for any positive integer $ n>m $, we have $ \chi(G^{\frac{m}{n}})=\omega(G^\frac{m}{n}) $.
In [1], it was shown that this conjecture is true in some special cases.

Keywords: chromatic number, fractional power of graph, clique number

Order-invariant queries ★★

Author(s): Segoufin

Question  
    \item Does $ {<}\text{-invariant\:FO} = \text{FO} $ hold over graphs of bounded tree-width? \item Is $ {<}\text{-invariant\:FO} $ included in $ \text{MSO} $ over graphs? \item Does $ {<}\text{-invariant\:FO} $ have a 0-1 law? \item Are properties of $ {<}\text{-invariant\:FO} $ Hanf-local? \item Is there a logic (with an effective syntax) that captures $ {<}\text{-invariant\:FO} $?

Keywords: Effective syntax; FMT12-LesHouches; Locality; MSO; Order invariance

Weak pentagon problem ★★

Author(s): Samal

Conjecture   If $ G $ is a cubic graph not containing a triangle, then it is possible to color the edges of $ G $ by five colors, so that the complement of every color class is a bipartite graph.

Keywords: Clebsch graph; cut-continuous mapping; edge-coloring; homomorphism; pentagon

Dice Dreams Cheats Generator Free Unlimited Cheats Generator (LATEST) ★★

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Dice Dreams Cheats Generator Free Unlimited Cheats Generator (LATEST)

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The Sims Mobile Cheats Generator Working Android Ios 2024 Cheats Generator (Newly Discovered) ★★

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The Sims Mobile Cheats Generator Working Android Ios 2024 Cheats Generator (Newly Discovered)

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Weak saturation of the cube in the clique

Author(s): Morrison; Noel

Problem  

Determine $ \text{wsat}(K_n,Q_3) $.

Keywords: bootstrap percolation; hypercube; Weak saturation

Fishing Clash Cheats Generator IOS Android No Verification 2024 (Tips Strategy) ★★

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Fishing Clash Cheats Generator IOS Android No Verification 2024 (Tips Strategy)

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Super Meat Boy Forever Points Cheats 2024 No Human Verification (Real) ★★

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Super Meat Boy Forever Points Cheats 2024 No Human Verification (Real)

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Approximation ratio for k-outerplanar graphs ★★

Author(s): Bentz

Conjecture   Is the approximation ratio for the Maximum Edge Disjoint Paths (MaxEDP) or the Maximum Integer Multiflow problem (MaxIMF) bounded by a constant in $ k $-outerplanar graphs or tree-width graphs?

Keywords: approximation algorithms; planar graph; polynomial algorithm

Circular choosability of planar graphs

Author(s): Mohar

Let $ G = (V, E) $ be a graph. If $ p $ and $ q $ are two integers, a $ (p,q) $-colouring of $ G $ is a function $ c $ from $ V $ to $ \{0,\dots,p-1\} $ such that $ q \le |c(u)-c(v)| \le p-q $ for each edge $ uv\in E $. Given a list assignment $ L $ of $ G $, i.e.~a mapping that assigns to every vertex $ v $ a set of non-negative integers, an $ L $-colouring of $ G $ is a mapping $ c : V \to N $ such that $ c(v)\in L(v) $ for every $ v\in V $. A list assignment $ L $ is a $ t $-$ (p,q) $-list-assignment if $ L(v) \subseteq \{0,\dots,p-1\} $ and $ |L(v)| \ge tq $ for each vertex $ v \in V $ . Given such a list assignment $ L $, the graph G is $ (p,q) $-$ L $-colourable if there exists a $ (p,q) $-$ L $-colouring $ c $, i.e. $ c $ is both a $ (p,q) $-colouring and an $ L $-colouring. For any real number $ t \ge 1 $, the graph $ G $ is $ t $-$ (p,q) $-choosable if it is $ (p,q) $-$ L $-colourable for every $ t $-$ (p,q) $-list-assignment $ L $. Last, $ G $ is circularly $ t $-choosable if it is $ t $-$ (p,q) $-choosable for any $ p $, $ q $. The circular choosability (or circular list chromatic number or circular choice number) of G is $$cch(G) := \inf\{t \ge 1 : G \text{ is circularly $t$-choosable}\}.$$

Problem   What is the best upper bound on circular choosability for planar graphs?

Keywords: choosability; circular colouring; planar graphs

Odd-cycle transversal in triangle-free graphs ★★

Author(s): Erdos; Faudree; Pach; Spencer

Conjecture   If $ G $ is a simple triangle-free graph, then there is a set of at most $ n^2/25 $ edges whose deletion destroys every odd cycle.

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The additive basis conjecture ★★★

Author(s): Jaeger; Linial; Payan; Tarsi

Conjecture   For every prime $ p $, there is a constant $ c(p) $ (possibly $ c(p)=p $) so that the union (as multisets) of any $ c(p) $ bases of the vector space $ ({\mathbb Z}_p)^n $ contains an additive basis.

Keywords: additive basis; matrix

The stubborn list partition problem ★★

Author(s): Cameron; Eschen; Hoang; Sritharan

Problem   Does there exist a polynomial time algorithm which takes as input a graph $ G $ and for every vertex $ v \in V(G) $ a subset $ \ell(v) $ of $ \{1,2,3,4\} $, and decides if there exists a partition of $ V(G) $ into $ \{A_1,A_2,A_3,A_4\} $ so that $ v \in A_i $ only if $ i \in \ell(v) $ and so that $ A_1,A_2 $ are independent, $ A_4 $ is a clique, and there are no edges between $ A_1 $ and $ A_3 $?

Keywords: list partition; polynomial algorithm

Closing Lemma for Diffeomorphism (Dynamical Systems) ★★★★

Author(s): Charles Pugh

Conjecture   Let $ f\in Diff^{r}(M) $ and $ p\in\omega_{f}  $. Then for any neighborhood $ V_{f}\subset Diff^{r}(M)  $ there is $ g\in V_{f} $ such that $ p $ is periodic point of $ g $

There is an analogous conjecture for flows ( $ C^{r} $ vector fields . In the case of diffeos this was proved by Charles Pugh for $ r = 1 $. In the case of Flows this has been solved by Sushei Hayahshy for $ r = 1 $ . But in the two cases the problem is wide open for $ r > 1 $

Keywords: Dynamics , Pertubation

Geometry Dash Free Gold Coins Stars Cheats 2024 (LEGIT) ★★

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Geometry Dash Free Gold Coins Stars Cheats 2024 (LEGIT)

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Fishdom Cheats Generator Cheats Generator 2023-2024 (Free!!) ★★

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Fishdom Cheats Generator Cheats Generator 2023-2024 (Free!!)

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Quartic rationally derived polynomials ★★★

Author(s): Buchholz; MacDougall

Call a polynomial $ p \in {\mathbb Q}[x] $ rationally derived if all roots of $ p $ and the nonzero derivatives of $ p $ are rational.

Conjecture   There does not exist a quartic rationally derived polynomial $ p \in {\mathbb Q}[x] $ with four distinct roots.

Keywords: derivative; diophantine; elliptic; polynomial

Highly arc transitive two ended digraphs ★★

Author(s): Cameron; Praeger; Wormald

Conjecture   If $ G $ is a highly arc transitive digraph with two ends, then every tile of $ G $ is a disjoint union of complete bipartite graphs.

Keywords: arc transitive; digraph; infinite graph

List Colourings of Complete Multipartite Graphs with 2 Big Parts ★★

Author(s): Allagan

Question   Given $ a,b\geq2 $, what is the smallest integer $ t\geq0 $ such that $ \chi_\ell(K_{a,b}+K_t)= \chi(K_{a,b}+K_t) $?

Keywords: complete bipartite graph; complete multipartite graph; list coloring

MacEachen Conjecture

Author(s): McEachen

Conjecture   Every odd prime number must either be adjacent to, or a prime distance away from a primorial or primorial product.

Keywords: primality; prime distribution

Counterexamples to the Baillie-PSW primality test ★★

Author(s):

Problem  (1)   Find a counterexample to Baillie-PSW primality test or prove that there is no one.
Problem  (2)   Find a composite $ n\equiv 3 $ or $ 7\pmod{10} $ which divides both $ 2^{n-1} - 1 $ (see Fermat pseudoprime) and the Fibonacci number $ F_{n+1} $ (see Lucas pseudoprime), or prove that there is no such $ n $.

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The three 4-flows conjecture ★★

Author(s): DeVos

Conjecture   For every graph $ G $ with no bridge, there exist three disjoint sets $ A_1,A_2,A_3 \subseteq E(G) $ with $ A_1 \cup A_2 \cup A_3 = E(G) $ so that $ G \setminus A_i $ has a nowhere-zero 4-flow for $ 1 \le i \le 3 $.

Keywords: nowhere-zero flow

Free Geometry Dash Cheats Gold Coins Stars Generator 2023-2024 ★★

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Free Geometry Dash Cheats Gold Coins Stars Generator 2023-2024

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Geometry Dash Free Gold Coins Stars Cheats 2024 (FREE!) ★★

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Geometry Dash Free Gold Coins Stars Cheats 2024 (FREE!)

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Bouchet's 6-flow conjecture ★★★

Author(s): Bouchet

Conjecture   Every bidirected graph with a nowhere-zero $ k $-flow for some $ k $, has a nowhere-zero $ 6 $-flow.

Keywords: bidirected graph; nowhere-zero flow

Durer's Conjecture ★★★

Author(s): Durer; Shephard

Conjecture   Every convex polytope has a non-overlapping edge unfolding.

Keywords: folding; polytope

The Alon-Tarsi basis conjecture ★★

Author(s): Alon; Linial; Meshulam

Conjecture   If $ B_1,B_2,\ldots B_p $ are invertible $ n \times n $ matrices with entries in $ {\mathbb Z}_p $ for a prime $ p $, then there is a $ n \times (p-1)n $ submatrix $ A $ of $ [B_1 B_2 \ldots B_p] $ so that $ A $ is an AT-base.

Keywords: additive basis; matrix

Burnside problem ★★★★

Author(s): Burnside

Conjecture   If a group has $ r $ generators and exponent $ n $, is it necessarily finite?

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Golf Battle Free Cheats Generator 999,999k Free 2024 (Free Generator) ★★

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Golf Battle Free Cheats Generator 999,999k Free 2024 (Free Generator)

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Something like Picard for 1-forms ★★

Author(s): Elsner

Conjecture   Let $ D $ be the open unit disk in the complex plane and let $ U_1,\dots,U_n $ be open sets such that $ \bigcup_{j=1}^nU_j=D\setminus\{0\} $. Suppose there are injective holomorphic functions $ f_j : U_j \to \mathbb{C}, $ $ j=1,\ldots,n, $ such that for the differentials we have $ {\rm d}f_j={\rm d}f_k $ on any intersection $ U_j\cap U_k $. Then those differentials glue together to a meromorphic 1-form on $ D $.

Keywords: Essential singularity; Holomorphic functions; Picard's theorem; Residue of 1-form; Riemann surfaces

KPZ Universality Conjecture ★★

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KPZ Universality Conjecture

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Latest Bingo Blitz Cheats Generator 999K Credits Free 2024 in 5 minutes (Up To) ★★

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Latest Bingo Blitz Cheats Generator 999K Credits Free 2024 in 5 minutes (Up To)

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World of Warships Cheats Generator Fully Works No Survey Cheats Generator (2024) ★★

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World of Warships Cheats Generator Fully Works No Survey Cheats Generator (2024)

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3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime ★★

Author(s):

Conjecture   $ 3~ $ is a primitive root modulo $ ~p $ for all primes $ ~p=16\cdot q^4+1 $, where $ ~q>3 $ is prime.

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Dividing up the unrestricted partitions ★★

Author(s): David S.; Newman

Begin with the generating function for unrestricted partitions:

(1+x+x^2+...)(1+x^2+x^4+...)(1+x^3+x^6+...)...

Now change some of the plus signs to minus signs. The resulting series will have coefficients congruent, mod 2, to the coefficients of the generating series for unrestricted partitions. I conjecture that the signs may be chosen such that all the coefficients of the series are either 1, -1, or zero.

Keywords: congruence properties; partition

V-Bucks Generator Unlimited Generator (No Human Verification) ★★

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V-Bucks Generator Unlimited Generator (No Human Verification)

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Asymptotic Distribution of Form of Polyhedra ★★

Author(s): Rüdinger

Problem   Consider the set of all topologically inequivalent polyhedra with $ k $ edges. Define a form parameter for a polyhedron as $ \beta:= v/(k+2) $ where $ v $ is the number of vertices. What is the distribution of $ \beta $ for $ k \to \infty $?

Keywords: polyhedral graphs, distribution

FarmVille 2 Coins Farm Bucks Cheats in a few minutes new 2024 (No Survey) ★★

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FarmVille 2 Coins Farm Bucks Cheats in a few minutes new 2024 (No Survey)

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Free Sims FreePlay Free Simoleons Life Points and Social Points Cheats 2024 (Safe) ★★

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Free Sims FreePlay Free Simoleons Life Points and Social Points Cheats 2024 (Safe)

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A homomorphism problem for flows ★★

Author(s): DeVos

Conjecture   Let $ M,M' $ be abelian groups and let $ B \subseteq M $ and $ B' \subseteq M' $ satisfy $ B=-B $ and $ B' = -B' $. If there is a homomorphism from $ Cayley(M,B) $ to $ Cayley(M',B') $, then every graph with a B-flow has a B'-flow.

Keywords: homomorphism; nowhere-zero flow; tension