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Dragon City Cheats Generator 2024 Update Hacks (Verified) ★★

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Dragon City Cheats Generator 2024 Update Hacks (Verified)

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Lindelöf hypothesis ★★

Author(s): Lindelöf

Conjecture   For any $ \epsilon>0 $ $$\zeta\left(\frac12 + it\right) \mbox{ is }\mathcal{O}(t^\epsilon).$$

Since $ \epsilon $ can be replaced by a smaller value, we can also write the conjecture as, for any positive $ \epsilon $, $$\zeta\left(\frac12 + it\right) \mbox{ is }o(t^\varepsilon).$$

Keywords: Riemann Hypothesis; zeta

Dragon City Cheats Generator 2023-2024 Edition (Verified) ★★

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Dragon City Cheats Generator 2023-2024 Edition (Verified)

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Lords Mobile Gems Coins Cheats Mod Android Ios No Survey 2024 (NEW) ★★

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Lords Mobile Gems Coins Cheats Mod Android Ios No Survey 2024 (NEW)

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New Update: Sims FreePlay Free Simoleons Life Points and Social Points Cheats 2024 No Human Verification ★★

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New Update: Sims FreePlay Free Simoleons Life Points and Social Points Cheats 2024 No Human Verification

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Free Coin Master Cheats No Human Verification No Survey (2024 Method) ★★

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Free Coin Master Cheats No Human Verification No Survey (2024 Method)

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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

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

Transversal achievement game on a square grid ★★

Author(s): Erickson

Problem   Two players alternately write O's (first player) and X's (second player) in the unoccupied cells of an $ n \times  n $ grid. The first player (if any) to occupy a set of $ n $ cells having no two cells in the same row or column is the winner. What is the outcome of the game given optimal play?

Keywords: game

Chromatic number of $\frac{3}{3}$-power of graph ★★

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Let $ G $ be a graph and $ m,n\in \mathbb{N} $. The graph $ G^{\frac{m}{n}} $ is defined to be the $ m $-power of the $ n $-subdivision of $ G $. In other words, $ G^{\frac{m}{n}}=(G^{\frac{1}{n}})^m $.

Conjecture   Let $ G $ be a graph with $ \Delta(G)\geq 2 $. Then $ \chi(G^{\frac{3}{3}})\leq 2\Delta(G)+1 $.

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Every metamonovalued funcoid is monovalued ★★

Author(s): Porton

Conjecture   Every metamonovalued funcoid is monovalued.

The reverse is almost trivial: Every monovalued funcoid is metamonovalued.

Keywords: monovalued

"Working Cheats" Subway Surfers Coins Keys Generator Ios Android 2024 ★★

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"Working Cheats" Subway Surfers Coins Keys Generator Ios Android 2024

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Working Apex Legends Cheats Online Coins Generator (No Survey) ★★

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Working Apex Legends Cheats Online Coins Generator (No Survey)

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Pebbling a cartesian product ★★★

Author(s): Graham

We let $ p(G) $ denote the pebbling number of a graph $ G $.

Conjecture   $ p(G_1 \Box G_2) \le p(G_1) p(G_2) $.

Keywords: pebbling; zero sum

The Borodin-Kostochka Conjecture ★★

Author(s): Borodin; Kostochka

Conjecture   Every graph with maximum degree $ \Delta \geq 9 $ has chromatic number at most $ \max\{\Delta-1, \omega\} $.

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Free Warframe Cheats Platinum Generator 2024 (Legal) ★★

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Free Warframe Cheats Platinum Generator 2024 (Legal)

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Match Masters Coins Cheats 2024 Update (FREE!!) ★★

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Match Masters Coins Cheats 2024 Update (FREE!!)

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Consecutive non-orientable embedding obstructions ★★★

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Conjecture   Is there a graph $ G $ that is a minor-minimal obstruction for two non-orientable surfaces?

Keywords: minor; surface

Complete bipartite subgraphs of perfect graphs ★★

Author(s): Fox

Problem   Let $ G $ be a perfect graph on $ n $ vertices. Is it true that either $ G $ or $ \bar{G} $ contains a complete bipartite subgraph with bipartition $ (A,B) $ so that $ |A|, |B| \ge n^{1 - o(1)} $?

Keywords: perfect graph

Hamiltonian cycles in line graphs of infinite graphs ★★

Author(s): Georgakopoulos

Conjecture  
    \item If $ G $ is a 4-edge-connected locally finite graph, then its line graph is hamiltonian. \item If the line graph $ L(G) $ of a locally finite graph $ G $ is 4-connected, then $ L(G) $ is hamiltonian.

Keywords: hamiltonian; infinite graph; line graphs

Monadic second-order logic with cardinality predicates ★★

Author(s): Courcelle

The problem concerns the extension of Monadic Second Order Logic (over a binary relation representing the edge relation) with the following atomic formulas:

    \item $ \text{``}\,\mathrm{Card}(X) = \mathrm{Card}(Y)\,\text{''} $ \item $ \text{``}\,\mathrm{Card}(X) \text{ belongs to } A\,\text{''} $

where $ A $ is a fixed recursive set of integers.

Let us fix $ k $ and a closed formula $ F $ in this language.

Conjecture   Is it true that the validity of $ F $ for a graph $ G $ of tree-width at most $ k $ can be tested in polynomial time in the size of $ G $?

Keywords: bounded tree width; cardinality predicates; FMT03-Bedlewo; MSO

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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Cooking Fever Cheats Generator Free 2024 in 5 minutes (New Cheats Generator Cooking Fever) ★★

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Cooking Fever Cheats Generator Free 2024 in 5 minutes (New Cheats Generator Cooking Fever)

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Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator (New 2024) ★★

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Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator (New 2024)

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A generalization of Vizing's Theorem? ★★

Author(s): Rosenfeld

Conjecture   Let $ H $ be a simple $ d $-uniform hypergraph, and assume that every set of $ d-1 $ points is contained in at most $ r $ edges. Then there exists an $ r+d-1 $-edge-coloring so that any two edges which share $ d-1 $ vertices have distinct colors.

Keywords: edge-coloring; hypergraph; Vizing

Approximation Ratio for Maximum Edge Disjoint Paths problem ★★

Author(s): Bentz

Conjecture   Can the approximation ratio $ O(\sqrt{n}) $ be improved for the Maximum Edge Disjoint Paths problem (MaxEDP) in planar graphs or can an inapproximability result stronger than $ \mathcal{APX} $-hardness?

Keywords: approximation algorithms; Disjoint paths; planar graph; polynomial algorithm

Average diameter of a bounded cell of a simple arrangement ★★

Author(s): Deza; Terlaky; Zinchenko

Conjecture   The average diameter of a bounded cell of a simple arrangement defined by $ n $ hyperplanes in dimension $ d $ is not greater than $ d $.

Keywords: arrangement; diameter; polytope

Partial List Coloring ★★★

Author(s): Albertson; Grossman; Haas

Conjecture   Let $ G $ be a simple graph with $ n $ vertices and list chromatic number $ \chi_\ell(G) $. Suppose that $ 0\leq t\leq \chi_\ell $ and each vertex of $ G $ is assigned a list of $ t $ colors. Then at least $ \frac{tn}{\chi_\ell(G)} $ vertices of $ G $ can be colored from these lists.

Keywords: list assignment; list coloring

Easy! Unlimited Rise Of Kingdoms Cheats Generator codes (GLITCH) ★★

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Easy! Unlimited Rise Of Kingdoms Cheats Generator codes (GLITCH)

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Legal SimCity BuildIt Cheats Generator No Human Verification 2024 (No Surveys Needed) ★★

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Legal SimCity BuildIt Cheats Generator No Human Verification 2024 (No Surveys Needed)

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Hungry Shark World Cheats Generator (Working Hungry Shark World Cheats Generator 2024) ★★

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Hungry Shark World Cheats Generator (Working Hungry Shark World Cheats Generator 2024)

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War Thunder Unlimited Golden Eagles Cheats Generator 2024 (fresh strategy) ★★

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War Thunder Unlimited Golden Eagles Cheats Generator 2024 (fresh strategy)

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General position subsets ★★

Author(s): Gowers

Question   What is the least integer $ f(n) $ such that every set of at least $ f(n) $ points in the plane contains $ n $ collinear points or a subset of $ n $ points in general position (no three collinear)?

Keywords: general position subset, no-three-in-line problem

The permanent conjecture ★★

Author(s): Kahn

Conjecture   If $ A $ is an invertible $ n \times n $ matrix, then there is an $ n \times n $ submatrix $ B $ of $ [A A] $ so that $ perm(B) $ is nonzero.

Keywords: invertible; matrix; permanent

Beneš Conjecture ★★★

Author(s): Beneš

Let $ E $ be a non-empty finite set. Given a partition $ \bf h $ of $ E $, the stabilizer of $ \bf h $, denoted $ S(\bf h) $, is the group formed by all permutations of $ E $ preserving each block of $ \mathbf h $.

Problem  ($ \star $)   Find a sufficient condition for a sequence of partitions $ {\bf h}_1, \dots, {\bf h}_\ell $ of $ E $ to be complete, i.e. such that the product of their stabilizers $ S({\bf h}_1) S({\bf h}_2) \dots S({\bf h}_\ell) $ is equal to the whole symmetric group $ \frak S(E) $ on $ E $. In particular, what about completeness of the sequence $ \bf h,\delta(\bf h),\dots,\delta^{\ell-1}(\bf h) $, given a partition $ \bf h $ of $ E $ and a permutation $ \delta $ of $ E $?
Conjecture  (Beneš)   Let $ \bf u $ be a uniform partition of $ E $ and $ \varphi $ be a permutation of $ E $ such that $ \bf u\wedge\varphi(\bf u)=\bf 0 $. Suppose that the set $ \big(\varphi S({\bf u})\big)^{n} $ is transitive, for some integer $ n\ge2 $. Then $$ \frak S(E) = \big(\varphi S({\bf u})\big)^{2n-1}. $$

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List Total Colouring Conjecture ★★

Author(s): Borodin; Kostochka; Woodall

Conjecture   If $ G $ is the total graph of a multigraph, then $ \chi_\ell(G)=\chi(G) $.

Keywords: list coloring; Total coloring; total graphs

Pentagon problem ★★★

Author(s): Nesetril

Question   Let $ G $ be a 3-regular graph that contains no cycle of length shorter than $ g $. Is it true that for large enough~$ g $ there is a homomorphism $ G \to C_5 $?

Keywords: cubic; homomorphism

Are different notions of the crossing number the same? ★★★

Author(s): Pach; Tóth

Problem   Does the following equality hold for every graph $ G $? \[ \text{pair-cr}(G) = \text{cr}(G) \]

The crossing number $ \text{cr}(G) $ of a graph $ G $ is the minimum number of edge crossings in any drawing of $ G $ in the plane. In the pairwise crossing number $ \text{pair-cr}(G) $, we minimize the number of pairs of edges that cross.

Keywords: crossing number; pair-crossing number

Equality in a matroidal circumference bound ★★

Author(s): Oxley; Royle

Question   Is the binary affine cube $ AG(3,2) $ the only 3-connected matroid for which equality holds in the bound $$E(M) \leq c(M) c(M^*) / 2$$ where $ c(M) $ is the circumference (i.e. largest circuit size) of $ M $?

Keywords: circumference

Snevily's conjecture ★★★

Author(s): Snevily

Conjecture   Let $ G $ be an abelian group of odd order and let $ A,B \subseteq G $ satisfy $ |A| = |B| = k $. Then the elements of $ A $ and $ B $ may be ordered $ A = \{a_1,\ldots,a_k\} $ and $ B = \{b_1,\ldots,b_k\} $ so that the sums $ a_1+b_1, a_2+b_2 \ldots, a_k + b_k $ are pairwise distinct.

Keywords: addition table; latin square; transversal

Shuffle-Exchange Conjecture ★★

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Shuffle-Exchange Conjecture

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Cyclic spanning subdigraph with small cyclomatic number ★★

Author(s): Bondy

Conjecture   Let $ D $ be a digraph all of whose strong components are nontrivial. Then $ D $ contains a cyclic spanning subdigraph with cyclomatic number at most $ \alpha(D) $.

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Ryser's conjecture ★★★

Author(s): Ryser

Conjecture   Let $ H $ be an $ r $-uniform $ r $-partite hypergraph. If $ \nu $ is the maximum number of pairwise disjoint edges in $ H $, and $ \tau $ is the size of the smallest set of vertices which meets every edge, then $ \tau \le (r-1) \nu $.

Keywords: hypergraph; matching; packing

Lucas Numbers Modulo m ★★

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Conjecture   The sequence {L(n) mod m}, where L(n) are the Lucas numbers, contains a complete residue system modulo m if and only if m is one of the following: 2, 4, 6, 7, 14, 3^k, k >=1.

Keywords: Lucas numbers

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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Hilbert-Smith conjecture ★★

Author(s): David Hilbert; Paul A. Smith

Conjecture   Let $ G $ be a locally compact topological group. If $ G $ has a continuous faithful group action on an $ n $-manifold, then $ G $ is a Lie group.

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3-Colourability of Arrangements of Great Circles ★★

Author(s): Felsner; Hurtado; Noy; Streinu

Consider a set $ S $ of great circles on a sphere with no three circles meeting at a point. The arrangement graph of $ S $ has a vertex for each intersection point, and an edge for each arc directly connecting two intersection points. So this arrangement graph is 4-regular and planar.

Conjecture   Every arrangement graph of a set of great circles is $ 3 $-colourable.

Keywords: arrangement graph; graph coloring

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

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

Free Bloons TD Battles Energy Medal Money Cheats Pro Apk 2024 (Android Ios) ★★

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Free Bloons TD Battles Energy Medal Money Cheats Pro Apk 2024 (Android Ios)

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