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The Sims Mobile Cheats Generator 2024 New Working Cheats Generator (New Method) ★★

Author(s):

The Sims Mobile Cheats Generator 2024 New Working Cheats Generator (New Method)

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Outward reloid of composition vs composition of outward reloids ★★

Author(s): Porton

Conjecture   For every composable funcoids $ f $ and $ g $ $$(\mathsf{RLD})_{\mathrm{out}}(g\circ f)\sqsupseteq(\mathsf{RLD})_{\mathrm{out}}g\circ(\mathsf{RLD})_{\mathrm{out}}f.$$

Keywords: outward reloid

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

Long rainbow arithmetic progressions ★★

Author(s): Fox; Jungic; Mahdian; Nesetril; Radoicic

For $ k\in \mathbb{N} $ let $ T_k $ denote the minimal number $ t\in \mathbb{N} $ such that there is a rainbow $ AP(k) $ in every equinumerous $ t $-coloring of $ \{ 1,2,\ldots ,tn\} $ for every $ n\in \mathbb{N} $

Conjecture   For all $ k\geq 3 $, $ T_k=\Theta (k^2) $.

Keywords: arithmetic progression; rainbow

The Crossing Number of the Complete Bipartite Graph ★★★

Author(s): Turan

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

Conjecture   $ \displaystyle   cr(K_{m,n}) = \floor{\frac m2} \floor{\frac {m-1}2}                      \floor{\frac n2} \floor{\frac {n-1}2}  $

Keywords: complete bipartite graph; crossing number

Coin Master Spins Coins Cheats 2024 No Human Verification (Real) ★★

Author(s):

Coin Master Spins Coins Cheats 2024 No Human Verification (Real)

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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

Chromatic Number of Common Graphs ★★

Author(s): Hatami; Hladký; Kráľ; Norine; Razborov

Question   Do common graphs have bounded chromatic number?

Keywords: common graph

Is Skewes' number e^e^e^79 an integer? ★★

Author(s):

Conjecture  

Skewes' number $ e^{e^{e^{79}}} $ is not an integer.

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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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Simplexity of the n-cube ★★★

Author(s):

Question   What is the minimum cardinality of a decomposition of the $ n $-cube into $ n $-simplices?

Keywords: cube; decomposition; simplex

Apex Legends Coins Cheats 2024 (rejuvenated cheats) ★★

Author(s):

Apex Legends Coins Cheats 2024 (rejuvenated cheats)

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Mapping planar graphs to odd cycles ★★★

Author(s): Jaeger

Conjecture   Every planar graph of girth $ \ge 4k $ has a homomorphism to $ C_{2k+1} $.

Keywords: girth; homomorphism; planar graph

Free Warframe Cheats Platinum Generator 2024 (Legal) ★★

Author(s):

Free Warframe Cheats Platinum Generator 2024 (Legal)

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Imbalance conjecture ★★

Author(s): Kozerenko

Conjecture   Suppose that for all edges $ e\in E(G) $ we have $ imb(e)>0 $. Then $ M_{G} $ is graphic.

Keywords: edge imbalance; graphic sequences

"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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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

Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!) ★★

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Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!)

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Waring rank of determinant ★★

Author(s): Teitler

Question   What is the Waring rank of the determinant of a $ d \times d $ generic matrix?

For simplicity say we work over the complex numbers. The $ d \times d $ generic matrix is the matrix with entries $ x_{i,j} $ for $ 1 \leq i,j \leq d $. Its determinant is a homogeneous form of degree $ d $, in $ d^2 $ variables. If $ F $ is a homogeneous form of degree $ d $, a power sum expression for $ F $ is an expression of the form $ F = \ell_1^d+\dotsb+\ell_r^d $, the $ \ell_i $ (homogeneous) linear forms. The Waring rank of $ F $ is the least number of terms $ r $ in any power sum expression for $ F $. For example, the expression $ xy = \frac{1}{4}(x+y)^2 - \frac{1}{4}(x-y)^2 $ means that $ xy $ has Waring rank $ 2 $ (it can't be less than $ 2 $, as $ xy \neq \ell_1^2 $).

The $ 2 \times 2 $ generic determinant $ x_{1,1}x_{2,2}-x_{1,2}x_{2,1} $ (or $ ad-bc $) has Waring rank $ 4 $. The Waring rank of the $ 3 \times 3 $ generic determinant is at least $ 14 $ and no more than $ 20 $, see for instance Lower bound for ranks of invariant forms, Example 4.1. The Waring rank of the permanent is also of interest. The comparison between the determinant and permanent is potentially relevant to Valiant's "VP versus VNP" problem.

Keywords: Waring rank, determinant

Universal Steiner triple systems ★★

Author(s): Grannell; Griggs; Knor; Skoviera

Problem   Which Steiner triple systems are universal?

Keywords: cubic graph; Steiner triple system

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

Coloring random subgraphs ★★

Author(s): Bukh

If $ G $ is a graph and $ p \in [0,1] $, we let $ G_p $ denote a subgraph of $ G $ where each edge of $ G $ appears in $ G_p $ with independently with probability $ p $.

Problem   Does there exist a constant $ c $ so that $ {\mathbb E}(\chi(G_{1/2})) > c \frac{\chi(G)}{\log \chi(G)} $?

Keywords: coloring; random graph

Monochromatic empty triangles ★★

Author(s):

Monochromatic empty triangles

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FarmVille 2 Cheats Coins Farm Bucks Generator Tested on iOS and Android (Latest Method) ★★

Author(s):

FarmVille 2 Cheats Coins Farm Bucks Generator Tested on iOS and Android (Latest Method)

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Easy! Unlimited Dragon City Cheats Generator codes (GLITCH) ★★

Author(s):

Easy! Unlimited Dragon City Cheats Generator codes (GLITCH)

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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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Directed path of length twice the minimum outdegree ★★★

Author(s): Thomassé

Conjecture   Every oriented graph with minimum outdegree $ k $ contains a directed path of length $ 2k $.

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Dense rational distance sets in the plane ★★★

Author(s): Ulam

Problem   Does there exist a dense set $ S \subseteq {\mathbb R}^2 $ so that all pairwise distances between points in $ S $ are rational?

Keywords: integral distance; rational distance

SimCity BuildIt Cheats Generator No Human Verification (Without Surveys) ★★

Author(s):

SimCity BuildIt Cheats Generator No Human Verification (Without Surveys)

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5-local-tensions ★★

Author(s): DeVos

Conjecture   There exists a fixed constant $ c $ (probably $ c=4 $ suffices) so that every embedded (loopless) graph with edge-width $ \ge c $ has a 5-local-tension.

Keywords: coloring; surface; tension

Marvel Strike Force Cheats Generator Android Ios 2024 Cheats Generator (improved version) ★★

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Marvel Strike Force Cheats Generator Android Ios 2024 Cheats Generator (improved version)

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Unused Free Bloons TD Battles Cheats No Human Verification No Survey (2024 Method) ★★

Author(s):

Unused Free Bloons TD Battles Cheats No Human Verification No Survey (2024 Method)

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The Riemann Hypothesis ★★★★

Author(s): Riemann

The zeroes of the Riemann zeta function that are inside the Critical Strip (i.e. the vertical strip of the complex plane where the real part of the complex variable is in ]0;1[), are actually located on the Critical line ( the vertical line of the complex plane with real part equal to 1/2)

Keywords: Millenium Problems; zeta

Sticky Cantor sets ★★

Author(s):

Conjecture   Let $ C $ be a Cantor set embedded in $ \mathbb{R}^n $. Is there a self-homeomorphism $ f $ of $ \mathbb{R}^n $ for every $ \epsilon $ greater than $ 0 $ so that $ f $ moves every point by less than $ \epsilon $ and $ f(C) $ does not intersect $ C $? Such an embedded Cantor set for which no such $ f $ exists (for some $ \epsilon $) is called "sticky". For what dimensions $ n $ do sticky Cantor sets exist?

Keywords: Cantor set

Subgraph of large average degree and large girth. ★★

Author(s): Thomassen

Conjecture   For all positive integers $ g $ and $ k $, there exists an integer $ d $ such that every graph of average degree at least $ d $ contains a subgraph of average degree at least $ k $ and girth greater than $ g $.

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Decomposition of completions of reloids ★★

Author(s): Porton

Conjecture   For composable reloids $ f $ and $ g $ it holds
    \item $ \operatorname{Compl} ( g \circ f) = ( \operatorname{Compl} g) \circ f $ if $ f $ is a co-complete reloid; \item $ \operatorname{CoCompl} ( f \circ g) = f \circ \operatorname{CoCompl} g $ if $ f $ is a complete reloid; \item $ \operatorname{CoCompl} ( ( \operatorname{Compl} g) \circ f) = \operatorname{Compl} ( g \circ   ( \operatorname{CoCompl} f)) = ( \operatorname{Compl} g) \circ ( \operatorname{CoCompl} f) $; \item $ \operatorname{Compl} ( g \circ ( \operatorname{Compl} f)) = \operatorname{Compl} ( g \circ   f) $; \item $ \operatorname{CoCompl} ( ( \operatorname{CoCompl} g) \circ f) = \operatorname{CoCompl} ( g   \circ f) $.

Keywords: co-completion; completion; reloid

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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Erdős-Posa property for long directed cycles ★★

Author(s): Havet; Maia

Conjecture   Let $ \ell \geq 2 $ be an integer. For every integer $ n\geq 0 $, there exists an integer $ t_n=t_n(\ell) $ such that for every digraph $ D $, either $ D $ has a $ n $ pairwise-disjoint directed cycles of length at least $ \ell $, or there exists a set $ T $ of at most $ t_n $ vertices such that $ D-T $ has no directed cycles of length at least $ \ell $.

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Free Gta 5 Cheats Generator Pro Apk (2024) ★★

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Free Gta 5 Cheats Generator Pro Apk (2024)

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Boom Beach Unlimited Generator Diamonds Cheats IOS And Android No Survey 2024 (free!!) ★★

Author(s):

Boom Beach Unlimited Generator Diamonds Cheats IOS And Android No Survey 2024 (free!!)

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Linial-Berge path partition duality ★★★

Author(s): Berge; Linial

Conjecture   The minimum $ k $-norm of a path partition on a directed graph $ D $ is no more than the maximal size of an induced $ k $-colorable subgraph.

Keywords: coloring; directed path; partition

Genshin Impact Generator Cheats without verification (Free) ★★

Author(s):

Genshin Impact Generator Cheats without verification (Free)

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Call Of Duty Mobile Cheats Generator 2024 (FREE!) ★★

Author(s):

Call Of Duty Mobile Cheats Generator 2024 (FREE!)

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MONOPOLY GO Cheats Generator IOS Android No Verification 2024 (fresh method) ★★

Author(s):

MONOPOLY GO Cheats Generator IOS Android No Verification 2024 (fresh method)

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Working Generator World Of Tanks Blitz Gold Credits Cheats Android Ios 2024 (HOT) ★★

Author(s):

Working Generator World Of Tanks Blitz Gold Credits Cheats Android Ios 2024 (HOT)

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Fishdom Cheats Generator 2024 Edition Update (WORKS) ★★

Author(s):

Fishdom Cheats Generator 2024 Edition Update (WORKS)

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Gardenscapes Cheats Generator Free Unlimited Cheats Generator (new codes Generator) ★★

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Gardenscapes Cheats Generator Free Unlimited Cheats Generator (new codes Generator)

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

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Dragon City Cheats Generator 2023-2024 Edition (Verified)

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

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Jurassic Park Builder Cheats Generator 2024 No Human Verification (Real)

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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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