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Jorgensen's Conjecture ★★★

Author(s): Jorgensen

Conjecture   Every 6-connected graph without a $ K_6 $ minor is apex (planar plus one vertex).

Keywords: connectivity; minor

Critical Ops Cheats 2024 Working (Credits Generator) ★★

Author(s):

Critical Ops Cheats 2024 Working (Credits Generator)

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SimCity BuildIt Generator Cheats Unlimited Resources No Jailbreak (Premium Orginal Generator) ★★

Author(s):

SimCity BuildIt Generator Cheats Unlimited Resources No Jailbreak (Premium Orginal Generator)

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Extremal $4$-Neighbour Bootstrap Percolation in the Hypercube ★★

Author(s): Morrison; Noel

Problem   Determine the smallest percolating set for the $ 4 $-neighbour bootstrap process in the hypercube.

Keywords: bootstrap percolation; extremal combinatorics; hypercube; percolation

List Hadwiger Conjecture ★★

Author(s): Kawarabayashi; Mohar

Conjecture   Every $ K_t $-minor-free graph is $ c t $-list-colourable for some constant $ c\geq1 $.

Keywords: Hadwiger conjecture; list colouring; minors

Monotone 4-term Arithmetic Progressions ★★

Author(s): Davis; Entringer; Graham; Simmons

Question   Is it true that every permutation of positive integers must contain monotone 4-term arithmetic progressions?

Keywords: monotone arithmetic progression; permutation

Discrete Logarithm Problem ★★★

Author(s):

If $ p $ is prime and $ g,h \in {\mathbb Z}_p^* $, we write $ \log_g(h) = n $ if $ n \in {\mathbb Z} $ satisfies $ g^n =  h $. The problem of finding such an integer $ n $ for a given $ g,h \in {\mathbb Z}^*_p $ (with $ g \neq 1 $) is the Discrete Log Problem.

Conjecture   There does not exist a polynomial time algorithm to solve the Discrete Log Problem.

Keywords: discrete log; NP

Mixing Circular Colourings

Author(s): Brewster; Noel

Question   Is $ \mathfrak{M}_c(G) $ always rational?

Keywords: discrete homotopy; graph colourings; mixing

Antichains in the cycle continuous order ★★

Author(s): DeVos

If $ G $,$ H $ are graphs, a function $ f : E(G) \rightarrow E(H) $ is called cycle-continuous if the pre-image of every element of the (binary) cycle space of $ H $ is a member of the cycle space of $ G $.

Problem   Does there exist an infinite set of graphs $ \{G_1,G_2,\ldots \} $ so that there is no cycle continuous mapping between $ G_i $ and $ G_j $ whenever $ i \neq j $ ?

Keywords: antichain; cycle; poset

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

Author(s):

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

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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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Idle Miner Tycoon Cheats Generator 2023-2024 (No Human Verification) ★★

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Idle Miner Tycoon Cheats Generator 2023-2024 (No Human Verification)

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New War Dragons Free Rubies Cheats 2024 Tested (extra) ★★

Author(s):

New War Dragons Free Rubies Cheats 2024 Tested (extra)

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Lovász Path Removal Conjecture ★★

Author(s): Lovasz

Conjecture   There is an integer-valued function $ f(k) $ such that if $ G $ is any $ f(k) $-connected graph and $ x $ and $ y $ are any two vertices of $ G $, then there exists an induced path $ P $ with ends $ x $ and $ y $ such that $ G-V(P) $ is $ k $-connected.

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Colouring the square of a planar graph ★★

Author(s): Wegner

Conjecture   Let $ G $ be a planar graph of maximum degree $ \Delta $. The chromatic number of its square is
    \item at most $ 7 $ if $ \Delta =3 $, \item at most $ \Delta+5 $ if $ 4\leq\Delta\leq 7 $, \item at most $ \left\lfloor\frac32\,\Delta\right\rfloor+1 $ if $ \Delta\ge8 $.

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House Of Fun Cheats Generator Free Unlimited Cheats Generator (new codes Generator) ★★

Author(s):

House Of Fun Cheats Generator Free Unlimited Cheats Generator (new codes Generator)

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The Double Cap Conjecture ★★

Author(s): Kalai

Conjecture   The largest measure of a Lebesgue measurable subset of the unit sphere of $ \mathbb{R}^n $ containing no pair of orthogonal vectors is attained by two open caps of geodesic radius $ \pi/4 $ around the north and south poles.

Keywords: combinatorial geometry; independent set; orthogonality; projective plane; sphere

A conjecture on iterated circumcentres ★★

Author(s): Goddyn

Conjecture   Let $ p_1,p_2,p_3,\ldots $ be a sequence of points in $ {\mathbb R}^d $ with the property that for every $ i \ge d+2 $, the points $ p_{i-1}, p_{i-2}, \ldots p_{i-d-1} $ are distinct, lie on a unique sphere, and further, $ p_i $ is the center of this sphere. If this sequence is periodic, must its period be $ 2d+4 $?

Keywords: periodic; plane geometry; sequence

Dragon City Cheats Generator without verification (Free) ★★

Author(s):

Dragon City Cheats Generator without verification (Free)

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Exponential Algorithms for Knapsack ★★

Author(s): Lipton

Conjecture  

The famous 0-1 Knapsack problem is: Given $ a_{1},a_{2},\dots,a_{n} $ and $ b $ integers, determine whether or not there are $ 0-1 $ values $ x_{1},x_{2},\dots,x_{n} $ so that $$ \sum_{i=1}^{n} a_{i}x_{i} = b.$$ The best known worst-case algorithm runs in time $ 2^{n/2} $ times a polynomial in $ n $. Is there an algorithm that runs in time $ 2^{n/3} $?

Keywords: Algorithm construction; Exponential-time algorithm; Knapsack

Which homology 3-spheres bound homology 4-balls? ★★★★

Author(s): Ancient/folklore

Problem   Is there a complete and computable set of invariants that can determine which (rational) homology $ 3 $-spheres bound (rational) homology $ 4 $-balls?

Keywords: cobordism; homology ball; homology sphere

Seymour's self-minor conjecture ★★★

Author(s): Seymour

Conjecture   Every infinite graph is a proper minor of itself.

Keywords: infinite graph; minor

Subgroup formed by elements of order dividing n ★★

Author(s): Frobenius

Conjecture  

Suppose $ G $ is a finite group, and $ n $ is a positive integer dividing $ |G| $. Suppose that $ G $ has exactly $ n $ solutions to $ x^{n} = 1 $. Does it follow that these solutions form a subgroup of $ G $?

Keywords: order, dividing

Bleach Brave Souls Cheats Generator No Human Verification (Ios Android) ★★

Author(s):

Bleach Brave Souls Cheats Generator No Human Verification (Ios Android)

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Dice Dreams Cheats Generator iOS Android (WORKING Generator) ★★

Author(s):

Dice Dreams Cheats Generator iOS Android (WORKING Generator)

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Working Generator Pokemon Go Pokecoins Cheats Android Ios 2024 (HOT) ★★

Author(s):

Working Generator Pokemon Go Pokecoins Cheats Android Ios 2024 (HOT)

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Arc-disjoint strongly connected spanning subdigraphs ★★

Author(s): Bang-Jensen; Yeo

Conjecture   There exists an ineteger $ k $ so that every $ k $-arc-connected digraph contains a pair of arc-disjoint strongly connected spanning subdigraphs?

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Are all Fermat Numbers square-free? ★★★

Author(s):

Conjecture   Are all Fermat Numbers \[ F_n  = 2^{2^{n } }  + 1 \] Square-Free?

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The robustness of the tensor product ★★★

Author(s): Ben-Sasson; Sudan

Problem   Given two codes $ R,C $, their Tensor Product $ R \otimes C $ is the code that consists of the matrices whose rows are codewords of $ R $ and whose columns are codewords of $ C $. The product $ R \otimes C $ is said to be robust if whenever a matrix $ M $ is far from $ R \otimes C $, the rows (columns) of $ M $ are far from $ R $ ($ C $, respectively).

The problem is to give a characterization of the pairs $ R,C $ whose tensor product is robust.

Keywords: codes; coding; locally testable; robustness

New-mathod! Free Bloons TD Battles Energy Medal Money Cheats 2024 (No Human Verification) ★★

Author(s):

New-mathod! Free Bloons TD Battles Energy Medal Money Cheats 2024 (No Human Verification)

Keywords:

Acyclic edge-colouring ★★

Author(s): Fiamcik

Conjecture   Every simple graph with maximum degree $ \Delta $ has a proper $ (\Delta+2) $-edge-colouring so that every cycle contains edges of at least three distinct colours.

Keywords: edge-coloring

Shuffle-Exchange Conjecture ★★★

Author(s): Beneš; Folklore; Stone

Given integers $ k,n\ge2 $, let $ d(k,n) $ be the smallest integer $ d\ge2 $ such that the symmetric group $ \frak S $ on the set of all words of length $ n $ over a $ k $-letter alphabet can be generated as $ \frak S = (\sigma \frak G)^d:=\sigma\frak G \sigma\frak G \dots \sigma\frak G $ ($ d $ times), where $ \sigma\in \frak S $ is the shuffle permutation defined by $ \sigma(x_1 x_2 \dots x_{n}) = x_2 \dots x_{n} x_1 $, and $ \frak G $ is the exchange group consisting of all permutations in $ \frak S $ preserving the first $ n-1 $ letters in the words.

Problem  (SE)   Evaluate $ d(k,n) $.
Conjecture  (SE)   $ d(k,n)=2n-1 $, for all $ k,n\ge2 $.

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eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (Reedem Today) ★★

Author(s):

eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (Reedem Today)

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

Author(s):

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

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Matching cut and girth ★★

Author(s):

Question   For every $ d $ does there exists a $ g $ such that every graph with average degree smaller than $ d $ and girth at least $ g $ has a matching-cut?

Keywords: matching cut, matching, cut

Graham's conjecture on tree reconstruction ★★

Author(s): Graham

Problem   for every graph $ G $, we let $ L(G) $ denote the line graph of $ G $. Given that $ G $ is a tree, can we determine it from the integer sequence $ |V(G)|, |V(L(G))|, |V(L(L(G)))|, \ldots $?

Keywords: reconstruction; tree

Choice Number of k-Chromatic Graphs of Bounded Order ★★

Author(s): Noel

Conjecture   If $ G $ is a $ k $-chromatic graph on at most $ mk $ vertices, then $ \text{ch}(G)\leq \text{ch}(K_{m*k}) $.

Keywords: choosability; complete multipartite graph; list coloring

Fortnite Working Generator V-Bucks Generator (NEW AND FREE) ★★

Author(s):

Fortnite Working Generator V-Bucks Generator (NEW AND FREE)

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3-flow conjecture ★★★

Author(s): Tutte

Conjecture   Every 4-edge-connected graph has a nowhere-zero 3-flow.

Keywords: nowhere-zero flow

Subset-sums equality (pigeonhole version) ★★★

Author(s):

Problem   Let $ a_1,a_2,\ldots,a_n $ be natural numbers with $ \sum_{i=1}^n a_i < 2^n - 1 $. It follows from the pigeon-hole principle that there exist distinct subsets $ I,J \subseteq \{1,\ldots,n\} $ with $ \sum_{i \in I} a_i = \sum_{j \in J} a_j $. Is it possible to find such a pair $ I,J $ in polynomial time?

Keywords: polynomial algorithm; search problem

War Dragons Rubies Cheats 2024 (re-designed) ★★

Author(s):

War Dragons Rubies Cheats 2024 (re-designed)

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"Working Cheats" Warzone COD points Generator No Human Verification 2024 ★★

Author(s):

"Working Cheats" Warzone COD points Generator No Human Verification 2024

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Star Stable Free Star Coins Jorvik Coins Cheats 2024 Real Working New Method ★★

Author(s):

Star Stable Free Star Coins Jorvik Coins Cheats 2024 Real Working New Method

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Obstacle number of planar graphs

Author(s): Alpert; Koch; Laison

Does there exist a planar graph with obstacle number greater than 1? Is there some $ k $ such that every planar graph has obstacle number at most $ k $?

Keywords: graph drawing; obstacle number; planar graph; visibility graph

Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator IOS Android 2024 (get codes) ★★

Author(s):

Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator IOS Android 2024 (get codes)

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Wide partition conjecture ★★

Author(s): Chow; Taylor

Conjecture   An integer partition is wide if and only if it is Latin.

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Brawlhalla Cheats Generator 2024 No Human Veryfication (codes) ★★

Author(s):

Brawlhalla Cheats Generator 2024 No Human Veryfication (codes)

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Jacobian Conjecture ★★★

Author(s): Keller

Conjecture   Let $ k $ be a field of characteristic zero. A collection $ f_1,\ldots,f_n $ of polynomials in variables $ x_1,\ldots,x_n $ defines an automorphism of $ k^n $ if and only if the Jacobian matrix is a nonzero constant.

Keywords: Affine Geometry; Automorphisms; Polynomials

War Machines Cheats Free Coins Diamonds 2024 No Verification (Android iOS Mod) ★★

Author(s):

Conjecture  

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House Of Fun Cheats Generator (iOS Android 2024) ★★

Author(s):

House Of Fun Cheats Generator (iOS Android 2024)

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