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Rainbow Six Siege Cheats Generator Unlimited R6 No Jailbreak (Premium Orginal Generator) ★★

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Rainbow Six Siege Cheats Generator Unlimited R6 No Jailbreak (Premium Orginal Generator)

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Fishing Clash Cheats Generator Free in 2024 (Premium For Free) ★★

Author(s):

Fishing Clash Cheats Generator Free in 2024 (Premium For Free)

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Three-chromatic (0,2)-graphs ★★

Author(s): Payan

Question   Are there any (0,2)-graphs with chromatic number exactly three?

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Dice Dreams Cheats Generator Get Free Dice Dreams Cheats Generator 2024 (Brand New) ★★

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Dice Dreams Cheats Generator Get Free Dice Dreams Cheats Generator 2024 (Brand New)

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2-accessibility of primes ★★

Author(s): Landman; Robertson

Question   Is the set of prime numbers 2-accessible?

Keywords: monochromatic diffsequences; primes

My Singing Monsters Cheats Generator Android Ios 2024 Cheats Generator (re-designed) ★★

Author(s):

My Singing Monsters Cheats Generator Android Ios 2024 Cheats Generator (re-designed)

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Erdős–Straus conjecture ★★

Author(s): Erdos; Straus

Conjecture  

For all $ n > 2 $, there exist positive integers $ x $, $ y $, $ z $ such that $$1/x + 1/y + 1/z = 4/n$$.

Keywords: Egyptian fraction

Rainbow AP(4) in an almost equinumerous coloring ★★

Author(s): Conlon

Problem   Do 4-colorings of $ \mathbb{Z}_{p} $, for $ p $ a large prime, always contain a rainbow $ AP(4) $ if each of the color classes is of size of either $ \lfloor p/4\rfloor $ or $ \lceil p/4\rceil $?

Keywords: arithmetic progression; rainbow

Generalised Empty Hexagon Conjecture ★★

Author(s): Wood

Conjecture   For each $ \ell\geq3 $ there is an integer $ f(\ell) $ such that every set of at least $ f(\ell) $ points in the plane contains $ \ell $ collinear points or an empty hexagon.

Keywords: empty hexagon

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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Davenport's constant ★★★

Author(s):

For a finite (additive) abelian group $ G $, the Davenport constant of $ G $, denoted $ s(G) $, is the smallest integer $ t $ so that every sequence of elements of $ G $ with length $ \ge t $ has a nontrivial subsequence which sums to zero.

Conjecture   $ s( {\mathbb Z}_n^d) = d(n-1) + 1 $

Keywords: Davenport constant; subsequence sum; zero sum

Convex Equipartitions with Extreme Perimeter ★★

Author(s): Nandakumar

To divide a given 2D convex region C into a specified number n of convex pieces all of equal area (perimeters could be different) such that the total perimeter of pieces is (1) maximized (2) minimized.

Remark: It appears maximizing the total perimeter is the easier problem.

Keywords: convex equipartition

Perfect 2-error-correcting codes over arbitrary finite alphabets. ★★

Author(s):

Conjecture   Does there exist a nontrivial perfect 2-error-correcting code over any finite alphabet, other than the ternary Golay code?

Keywords: 2-error-correcting; code; existence; perfect; perfect code

Boom Beach Unlimited Diamonds Cheats Generator 2024 (fresh strategy) ★★

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Boom Beach Unlimited Diamonds Cheats Generator 2024 (fresh strategy)

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The Crossing Number of the Hypercube ★★

Author(s): Erdos; Guy

The crossing number $ cr(G) $ of $ G $ is the minimum number of crossings in all drawings of $ G $ in the plane.

The $ d $-dimensional (hyper)cube $ Q_d $ is the graph whose vertices are all binary sequences of length $ d $, and two of the sequences are adjacent in $ Q_d $ if they differ in precisely one coordinate.

Conjecture   $ \displaystyle \lim  \frac{cr(Q_d)}{4^d} = \frac{5}{32} $

Keywords: crossing number; hypercube

Reed's omega, delta, and chi conjecture ★★★

Author(s): Reed

For a graph $ G $, we define $ \Delta(G) $ to be the maximum degree, $ \omega(G) $ to be the size of the largest clique subgraph, and $ \chi(G) $ to be the chromatic number of $ G $.

Conjecture   $ \chi(G) \le \ceil{\frac{1}{2}(\Delta(G)+1) + \frac{1}{2}\omega(G)} $ for every graph $ G $.

Keywords: coloring

Dragon City Cheats Generator without verification (Free) ★★

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Dragon City Cheats Generator without verification (Free)

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Long directed cycles in diregular digraphs ★★★

Author(s): Jackson

Conjecture   Every strong oriented graph in which each vertex has indegree and outdegree at least $ d $ contains a directed cycle of length at least $ 2d+1 $.

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Hungry Shark Evolution Cheats Generator 2024 Cheats Generator Tested On Android Ios (WORKING TIPS) ★★

Author(s):

Hungry Shark Evolution Cheats Generator 2024 Cheats Generator Tested On Android Ios (WORKING TIPS)

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Chromatic number of random lifts of complete graphs ★★

Author(s): Amit

Question   Is the chromatic number of a random lift of $ K_5 $ concentrated on a single value?

Keywords: random lifts, coloring

Minimal graphs with a prescribed number of spanning trees ★★

Author(s): Azarija; Skrekovski

Conjecture   Let $ n \geq 3 $ be an integer and let $ \alpha(n) $ denote the least integer $ k $ such that there exists a simple graph on $ k $ vertices having precisely $ n $ spanning trees. Then $  \alpha(n) = o(\log{n}). $

Keywords: number of spanning trees, asymptotics

Barnette's Conjecture ★★★

Author(s): Barnette

Conjecture   Every 3-connected cubic planar bipartite graph is Hamiltonian.

Keywords: bipartite; cubic; hamiltonian

Algebraic independence of pi and e ★★★

Author(s):

Conjecture   $ \pi $ and $ e $ are algebraically independent

Keywords: algebraic independence

Super Meat Boy Forever Points Cheats No Human Verification (Ios Android) ★★

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Super Meat Boy Forever Points Cheats No Human Verification (Ios Android)

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World of Warships Cheats Generator Free Strategy 2024 (The Legit Method) ★★

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World of Warships Cheats Generator Free Strategy 2024 (The Legit Method)

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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

Outer reloid of restricted funcoid ★★

Author(s): Porton

Question   $ ( \mathsf{RLD})_{\mathrm{out}} (f \cap^{\mathsf{FCD}} ( \mathcal{A} \times^{\mathsf{FCD}} \mathcal{B})) = (( \mathsf{RLD})_{\mathrm{out}} f) \cap^{\mathsf{RLD}} ( \mathcal{A} \times^{\mathsf{RLD}} \mathcal{B}) $ for every filter objects $ \mathcal{A} $ and $ \mathcal{B} $ and a funcoid $ f\in\mathsf{FCD}(\mathrm{Src}\,f; \mathrm{Dst}\,f) $?

Keywords: direct product of filters; outer reloid

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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Bases of many weights ★★★

Author(s): Schrijver; Seymour

Let $ G $ be an (additive) abelian group, and for every $ S \subseteq G $ let $ {\mathit stab}(S) = \{ g \in G : g + S = S \} $.

Conjecture   Let $ M $ be a matroid on $ E $, let $ w : E \rightarrow G $ be a map, put $ S = \{ \sum_{b \in B} w(b) : B \mbox{ is a base} \} $ and $ H = {\mathit stab}(S) $. Then $$|S| \ge |H| \left( 1 - rk(M) + \sum_{Q \in G/H} rk(w^{-1}(Q)) \right).$$

Keywords: matroid; sumset; zero sum

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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Turán Problem for $10$-Cycles in the Hypercube ★★

Author(s): Erdos

Problem   Bound the extremal number of $ C_{10} $ in the hypercube.

Keywords: cycles; extremal combinatorics; hypercube

Working My Singing Monsters Cheats Generator Online (No Survey) ★★

Author(s):

Working My Singing Monsters Cheats Generator Online (No Survey)

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What is the smallest number of disjoint spanning trees made a graph Hamiltonian ★★

Author(s): Goldengorin

We are given a complete simple undirected weighted graph $ G_1=(V,E) $ and its first arbitrary shortest spanning tree $ T_1=(V,E_1) $. We define the next graph $ G_2=(V,E\setminus E_1) $ and find on $ G_2 $ the second arbitrary shortest spanning tree $ T_2=(V,E_2) $. We continue similarly by finding $ T_3=(V,E_3) $ on $ G_3=(V,E\setminus \cup_{i=1}^{2}E_i) $, etc. Let k be the smallest number of disjoint shortest spanning trees as defined above and let $ T^{k}=(V,\cup_{i=1}^{k}E_i) $ be the graph obtained as union of all $ k $ disjoint trees.

Question 1. What is the smallest number of disjoint spanning trees creates a graph $ T^{k} $ containing a Hamiltonian path.

Question 2. What is the smallest number of disjoint spanning trees creates a graph $ T^{k} $ containing a shortest Hamiltonian path?

Questions 3 and 4. Replace in questions 1 and 2 a shortest spanning tree by a 1-tree. What is the smallest number of disjoint 1-trees creates a Hamiltonian graph? What is the smallest number of disjoint 1-trees creates a graph containing a shortest Hamiltonian cycle?

Keywords: 1-trees; cycle; Hamitonian path; spanning trees

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

Match Masters Free Coins Cheats 2024 (LEGIT) ★★

Author(s):

Match Masters Free Coins Cheats 2024 (LEGIT)

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Lords Mobile Cheats Unlimited Gems Coins Generator (No Human Verification) ★★

Author(s):

Lords Mobile Cheats Unlimited Gems Coins Generator (No Human Verification)

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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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Durer's Conjecture ★★★

Author(s): Durer; Shephard

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

Keywords: folding; polytope

Hungry Shark World Cheats Generator 2024 (fresh strategy) ★★

Author(s):

Hungry Shark World Cheats Generator 2024 (fresh strategy)

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Rendezvous on a line ★★★

Author(s): Alpern

Problem   Two players start at a distance of 2 on an (undirected) line (so, neither player knows the direction of the other) and both move at a maximum speed of 1. What is the infimum expected meeting time $ R $ (first time when the players occupy the same point) which can be achieved assuming the two players must adopt the same strategy?

Keywords: game theory; optimization; rendezvous

Domination in plane triangulations ★★

Author(s): Matheson; Tarjan

Conjecture   Every sufficiently large plane triangulation $ G $ has a dominating set of size $ \le \frac{1}{4} |V(G)| $.

Keywords: coloring; domination; multigrid; planar graph; triangulation

Matchington Mansion Free Stars Coins Cheats Free Generator 2024 in 5 minutes (successive cheats) ★★

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Matchington Mansion Free Stars Coins Cheats Free Generator 2024 in 5 minutes (successive cheats)

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Free Clash of Clans Gems Cheats 2024 Edition Update (WORKS!) ★★

Author(s):

Free Clash of Clans Gems Cheats 2024 Edition Update (WORKS!)

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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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Cooking Fever Cheats Generator Android Ios No Survey 2024 (NEW) ★★

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Cooking Fever Cheats Generator Android Ios No Survey 2024 (NEW)

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Inverse Galois Problem ★★★★

Author(s): Hilbert

Conjecture   Every finite group is the Galois group of some finite algebraic extension of $ \mathbb Q $.

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New World Of Tanks Blitz Free Gold Credits Cheats 2024 Tested (extra) ★★

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New World Of Tanks Blitz Free Gold Credits Cheats 2024 Tested (extra)

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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

F_d versus F_{d+1} ★★★

Author(s): Krajicek

Problem   Find a constant $ k $ such that for any $ d $ there is a sequence of tautologies of depth $ k $ that have polynomial (or quasi-polynomial) size proofs in depth $ d+1 $ Frege system $ F_{d+1} $ but requires exponential size $ F_d $ proofs.

Keywords: Frege system; short proof

Unfriendly partitions ★★★

Author(s): Cowan; Emerson

If $ G $ is a graph, we say that a partition of $ V(G) $ is unfriendly if every vertex has at least as many neighbors in the other classes as in its own.

Problem   Does every countably infinite graph have an unfriendly partition into two sets?

Keywords: coloring; infinite graph; partition