Random

Raid Shadow Legends Cheats Generator 2024 (fresh strategy) ★★

Author(s):

Raid Shadow Legends Cheats Generator 2024 (fresh strategy)

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Earth-Moon Problem ★★

Author(s): Ringel

Problem   What is the maximum number of colours needed to colour countries such that no two countries sharing a common border have the same colour in the case where each country consists of one region on earth and one region on the moon ?

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Rank vs. Genus ★★★

Author(s): Johnson

Question   Is there a hyperbolic 3-manifold whose fundamental group rank is strictly less than its Heegaard genus? How much can the two differ by?

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Monochromatic empty triangles ★★

Author(s):

Monochromatic empty triangles

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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

REAL* Free!! Bloons TD Battles Energy Medal Money Cheats Trick 2024 ★★

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REAL* Free!! Bloons TD Battles Energy Medal Money Cheats Trick 2024

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The Bollobás-Eldridge-Catlin Conjecture on graph packing ★★★

Author(s):

Conjecture  (BEC-conjecture)   If $ G_1 $ and $ G_2 $ are $ n $-vertex graphs and $ (\Delta(G_1) + 1) (\Delta(G_2) + 1) < n + 1 $, then $ G_1 $ and $ G_2 $ pack.

Keywords: graph packing

Critical Ops Credits Cheats 2024 New Working Generator (New Method!) ★★

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Critical Ops Credits Cheats 2024 New Working Generator (New Method!)

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Decomposing an eulerian graph into cycles. ★★

Author(s): Hajós

Conjecture   Every simple eulerian graph on $ n $ vertices can be decomposed into at most $ \frac{1}{2}(n-1) $ cycles.

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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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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

Chromatic number of associahedron ★★

Author(s): Fabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood

Conjecture   Associahedra have unbounded chromatic number.

Keywords: associahedron, graph colouring, chromatic number

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

Author(s):

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

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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

Fundamental group torsion for subsets of Euclidean 3-space ★★

Author(s): Ancient/folklore

Problem   Does there exist a subset of $ \mathbb R^3 $ such that its fundamental group has an element of finite order?

Keywords: subsets of euclidean space; torsion

Fishing Clash Cheats Generator Free 2024 (New) ★★

Author(s):

Fishing Clash Cheats Generator Free 2024 (New)

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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

Refuting random 3SAT-instances on $O(n)$ clauses (weak form) ★★★

Author(s): Feige

Conjecture   For every rational $ \epsilon > 0 $ and every rational $ \Delta $, there is no polynomial-time algorithm for the following problem.

Given is a 3SAT (3CNF) formula $ I $ on $ n $ variables, for some $ n $, and $ m = \floor{\Delta n} $ clauses drawn uniformly at random from the set of formulas on $ n $ variables. Return with probability at least 0.5 (over the instances) that $ I $ is typical without returning typical for any instance with at least $ (1 - \epsilon)m $ simultaneously satisfiable clauses.

Keywords: NP; randomness in TCS; satisfiability

PK XD Generator Cheats 2024 Generator Cheats Tested On Android Ios (WORKING TIPS) ★★

Author(s):

PK XD Generator Cheats 2024 Generator Cheats Tested On Android Ios (WORKING TIPS)

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Which outer reloids are equal to inner ones ★★

Author(s): Porton

Warning: This formulation is vague (not exact).

Question   Characterize the set $ \{f\in\mathsf{FCD} \mid (\mathsf{RLD})_{\mathrm{in}} f=(\mathsf{RLD})_{\mathrm{out}} f\} $. In other words, simplify this formula.

The problem seems rather difficult.

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Partition of Complete Geometric Graph into Plane Trees ★★

Author(s):

Conjecture   Every complete geometric graph with an even number of vertices has a partition of its edge set into plane (i.e. non-crossing) spanning trees.

Keywords: complete geometric graph, edge colouring

Algorithm for graph homomorphisms ★★

Author(s): Fomin; Heggernes; Kratsch

Question  

Is there an algorithm that decides, for input graphs $ G $ and $ H $, whether there exists a homomorphism from $ G $ to $ H $ in time $ O(c^{|V(G)|+|V(H)|}) $ for some constant $ c $?

Keywords: algorithm; Exponential-time algorithm; homomorphism

KPZ Universality Conjecture ★★★

Author(s):

Conjecture   Formulate a central limit theorem for the KPZ universality class.

Keywords: KPZ equation, central limit theorem

Jurassic Park Builder Cheats Generator 2024 No Human Verification (Brand New) ★★

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Jurassic Park Builder Cheats Generator 2024 No Human Verification (Brand New)

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8 Ball Pool Free Cash Strategy 2024 (The Legit Method) ★★

Author(s):

8 Ball Pool Free Cash Strategy 2024 (The Legit Method)

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Criterion for boundedness of power series

Author(s): Rüdinger

Question   Give a necessary and sufficient criterion for the sequence $ (a_n) $ so that the power series $ \sum_{n=0}^{\infty} a_n x^n $ is bounded for all $ x \in \mathbb{R} $.

Keywords: boundedness; power series; real analysis

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

Author(s):

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

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Decomposing a connected graph into paths. ★★★

Author(s): Gallai

Conjecture   Every simple connected graph on $ n $ vertices can be decomposed into at most $ \frac{1}{2}(n+1) $ paths.

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Nearly spanning regular subgraphs ★★★

Author(s): Alon; Mubayi

Conjecture   For every $ \epsilon > 0 $ and every positive integer $ k $, there exists $ r_0 = r_0(\epsilon,k) $ so that every simple $ r $-regular graph $ G $ with $ r \ge r_0 $ has a $ k $-regular subgraph $ H $ with $ |V(H)| \ge (1- \epsilon) |V(G)| $.

Keywords: regular; subgraph

The circular embedding conjecture ★★★

Author(s): Haggard

Conjecture   Every 2-connected graph may be embedded in a surface so that the boundary of each face is a cycle.

Keywords: cover; cycle

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

Author(s):

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

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Cooking Fever Cheats Generator Latest Version 2024 For Free (WORKING Generator) ★★

Author(s):

Cooking Fever Cheats Generator Latest Version 2024 For Free (WORKING Generator)

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Partitionning a tournament into k-strongly connected subtournaments. ★★

Author(s): Thomassen

Problem   Let $ k_1, \dots , k_p $ be positve integer Does there exists an integer $ g(k_1, \dots , k_p) $ such that every $ g(k_1, \dots , k_p) $-strong tournament $ T $ admits a partition $ (V_1\dots , V_p) $ of its vertex set such that the subtournament induced by $ V_i $ is a non-trivial $ k_i $-strong for all $ 1\leq i\leq p $.

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Question about 'solving' something ★★

Author(s):

Conjecture  

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Toon Blast Cheats Generator 2024 (rejuvenated Generator) ★★

Author(s):

Toon Blast Cheats Generator 2024 (rejuvenated Generator)

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Complexity of square-root sum ★★

Author(s): Goemans

Question   What is the complexity of the following problem?

Given $ a_1,\dots,a_n; k $, determine whether or not $  \sum_i \sqrt{a_i} \leq k.  $

Keywords: semi-definite programming

FarmVille 2 Unlimited Coins Farm Bucks Cheats 2024 (WORKING IN 5 SECOND) ★★

Author(s):

FarmVille 2 Unlimited Coins Farm Bucks Cheats 2024 (WORKING IN 5 SECOND)

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Are all Mersenne Numbers with prime exponent square-free? ★★★

Author(s):

Conjecture   Are all Mersenne Numbers with prime exponent $ {2^p-1} $ Square free?

Keywords: Mersenne number

The Erdos-Turan conjecture on additive bases ★★★★

Author(s): Erdos; Turan

Let $ B \subseteq {\mathbb N} $. The representation function $ r_B : {\mathbb N} \rightarrow {\mathbb N} $ for $ B $ is given by the rule $ r_B(k) = \#\{ (i,j) \in B \times B : i + j = k \} $. We call $ B $ an additive basis if $ r_B $ is never $ 0 $.

Conjecture   If $ B $ is an additive basis, then $ r_B $ is unbounded.

Keywords: additive basis; representation function

Family Island Cheats Generator Pro Apk (Android Ios) ★★

Author(s):

Family Island Cheats Generator Pro Apk (Android Ios)

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Rainbow Six Siege Cheats Generator Free 2024 in 5 minutes (successive Generator) ★★

Author(s):

Rainbow Six Siege Cheats Generator Free 2024 in 5 minutes (successive Generator)

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KPZ Universality Conjecture ★★

Author(s):

KPZ Universality Conjecture

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Covering a square with unit squares ★★

Author(s):

Conjecture   For any integer $ n \geq 1 $, it is impossible to cover a square of side greater than $ n $ with $ n^2+1 $ unit squares.

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

Author(s):

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

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Shannon capacity of the seven-cycle ★★★

Author(s):

Problem   What is the Shannon capacity of $ C_7 $?

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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

New Update: Warzone Free COD points Cheats 2024 No Human Verification ★★

Author(s):

New Update: Warzone Free COD points Cheats 2024 No Human Verification

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Cycle Double Covers Containing Predefined 2-Regular Subgraphs ★★★

Author(s): Arthur; Hoffmann-Ostenhof

Conjecture   Let $ G $ be a $ 2 $-connected cubic graph and let $ S $ be a $ 2 $-regular subgraph such that $ G-E(S) $ is connected. Then $ G $ has a cycle double cover which contains $ S $ (i.e all cycles of $ S $).

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Random stable roommates ★★

Author(s): Mertens

Conjecture   The probability that a random instance of the stable roommates problem on $ n \in 2{\mathbb N} $ people admits a solution is $ \Theta( n ^{-1/4} ) $.

Keywords: stable marriage; stable roommates

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