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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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Signing a graph to have small magnitude eigenvalues ★★

Author(s): Bilu; Linial

Conjecture   If $ A $ is the adjacency matrix of a $ d $-regular graph, then there is a symmetric signing of $ A $ (i.e. replace some $ +1 $ entries by $ -1 $) so that the resulting matrix has all eigenvalues of magnitude at most $ 2 \sqrt{d-1} $.

Keywords: eigenvalue; expander; Ramanujan graph; signed graph; signing

Partial List Coloring ★★★

Author(s): Iradmusa

Let $ G $ be a simple graph, and for every list assignment $ \mathcal{L} $ let $ \lambda_{\mathcal{L}} $ be the maximum number of vertices of $ G $ which are colorable with respect to $ \mathcal{L} $. Define $ \lambda_t = \min{ \lambda_{\mathcal{L}} } $, where the minimum is taken over all list assignments $ \mathcal{L} $ with $ |\mathcal{L}| = t $ for all $ v \in V(G) $.

Conjecture   [2] Let $ G $ be a graph with list chromatic number $ \chi_\ell $ and $ 1\leq r\leq s\leq \chi_\ell $. Then \[\frac{\lambda_r}{r}\geq\frac{\lambda_s}{s}.\]

Keywords: list assignment; list coloring

Fixed-point logic with counting ★★

Author(s): Blass

Question   Can either of the following be expressed in fixed-point logic plus counting:
    \item Given a graph, does it have a perfect matching, i.e., a set $ M $ of edges such that every vertex is incident to exactly one edge from $ M $? \item Given a square matrix over a finite field (regarded as a structure in the natural way, as described in [BGS02]), what is its determinant?

Keywords: Capturing PTime; counting quantifiers; Fixed-point logic; FMT03-Bedlewo

Nonseparating planar continuum ★★

Author(s):

Conjecture   Does any path-connected, compact set in the plane which does not separate the plane have the fixed point property?

A set has the fixed point property if every continuous map from it into itself has a fixed point.

Keywords: fixed point

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

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New War Dragons Free Rubies Cheats 2024 Tested (extra)

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Star chromatic index of cubic graphs ★★

Author(s): Dvorak; Mohar; Samal

The star chromatic index $ \chi_s'(G) $ of a graph $ G $ is the minimum number of colors needed to properly color the edges of the graph so that no path or cycle of length four is bi-colored.

Question   Is it true that for every (sub)cubic graph $ G $, we have $ \chi_s'(G) \le 6 $?

Keywords: edge coloring; star 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

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

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Hungry Shark World Cheats Generator 2024 (fresh strategy)

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Fat 4-polytopes ★★★

Author(s): Eppstein; Kuperberg; Ziegler

The fatness of a 4-polytope $ P $ is defined to be $ (f_1 + f_2)/(f_0 + f_3) $ where $ f_i $ is the number of faces of $ P $ of dimension $ i $.

Question   Does there exist a fixed constant $ c $ so that every convex 4-polytope has fatness at most $ c $?

Keywords: f-vector; polytope

Yu Gi Oh Duel Links Cheats Generator 2024 Real Working (new method) ★★

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Yu Gi Oh Duel Links Cheats Generator 2024 Real Working (new method)

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Yu Gi Oh Duel Links Cheats Generator 2024 (safe and working) ★★

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Yu Gi Oh Duel Links Cheats Generator 2024 (safe and working)

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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

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

Real roots of the flow polynomial ★★

Author(s): Welsh

Conjecture   All real roots of nonzero flow polynomials are at most 4.

Keywords: flow polynomial; nowhere-zero flow

Critical Ops Cheats 2024 Working (Credits Generator) ★★

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Critical Ops Cheats 2024 Working (Credits Generator)

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Rise Of Kingdoms Cheats Generator 2024-2024 (NEW-FREE!!) ★★

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Rise Of Kingdoms Cheats Generator 2024-2024 (NEW-FREE!!)

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Smooth 4-dimensional Schoenflies problem ★★★★

Author(s): Alexander

Problem   Let $ M $ be a $ 3 $-dimensional smooth submanifold of $ S^4 $, $ M $ diffeomorphic to $ S^3 $. By the Jordan-Brouwer separation theorem, $ M $ separates $ S^4 $ into the union of two compact connected $ 4 $-manifolds which share $ M $ as a common boundary. The Schoenflies problem asks, are these $ 4 $-manifolds diffeomorphic to $ D^4 $? ie: is $ M $ unknotted?

Keywords: 4-dimensional; Schoenflies; sphere

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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Square achievement game on an n x n 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 four cells at the vertices of a square with horizontal and vertical sides is the winner. What is the outcome of the game given optimal play? Note: Roland Bacher and Shalom Eliahou proved that every 15 x 15 binary matrix contains four equal entries (all 0's or all 1's) at the vertices of a square with horizontal and vertical sides. So the game must result in a winner (the first player) when n=15.

Keywords: game

Decomposing an eulerian graph into cycles with no two consecutives edges on a prescribed eulerian tour. ★★

Author(s): Sabidussi

Conjecture   Let $ G $ be an eulerian graph of minimum degree $ 4 $, and let $ W $ be an eulerian tour of $ G $. Then $ G $ admits a decomposition into cycles none of which contains two consecutive edges of $ W $.

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Circular flow number of regular class 1 graphs ★★

Author(s): Steffen

A nowhere-zero $ r $-flow $ (D(G),\phi) $ on $ G $ is an orientation $ D $ of $ G $ together with a function $ \phi $ from the edge set of $ G $ into the real numbers such that $ 1 \leq |\phi(e)| \leq r-1 $, for all $ e \in E(G) $, and $ \sum_{e \in E^+(v)}\phi(e) = \sum_{e \in E^-(v)}\phi(e), \textrm{ for all } v \in V(G) $. The circular flow number of $ G $ is inf$ \{ r | G $ has a nowhere-zero $ r $-flow $ \} $, and it is denoted by $ F_c(G) $.

A graph with maximum vertex degree $ k $ is a class 1 graph if its edge chromatic number is $ k $.

Conjecture   Let $ t \geq 1 $ be an integer and $ G $ a $ (2t+1) $-regular graph. If $ G $ is a class 1 graph, then $ F_c(G) \leq 2 + \frac{2}{t} $.

Keywords: nowhere-zero flow, edge-colorings, regular graphs

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

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

Cheats Candy Crush Saga Golds Lives Generator 2023-2024 (NEW-FREE!!) ★★

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Cheats Candy Crush Saga Golds Lives Generator 2023-2024 (NEW-FREE!!)

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

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Jurassic Park Builder Cheats Generator No Human Verification No Survey (Method 2024)

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Geometry Dash Free Gold Coins Stars Cheats 2024 (LEGIT) ★★

Author(s):

Geometry Dash Free Gold Coins Stars Cheats 2024 (LEGIT)

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Rise Of Kingdoms Cheats Generator 2024 Update Hacks (Verified) ★★

Author(s):

Rise Of Kingdoms Cheats Generator 2024 Update Hacks (Verified)

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V-Bucks Generator Free 2024 in 5 minutes (New Generator V-Bucks) ★★

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V-Bucks Generator Free 2024 in 5 minutes (New Generator V-Bucks)

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Yu Gi Oh Duel Links Cheats Generator 2024 (No Human Verification) ★★

Author(s):

Yu Gi Oh Duel Links Cheats Generator 2024 (No Human Verification)

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Birch & Swinnerton-Dyer conjecture ★★★★

Author(s):

Conjecture   Let $ E/K $ be an elliptic curve over a number field $ K $. Then the order of the zeros of its $ L $-function, $ L(E, s) $, at $ s = 1 $ is the Mordell-Weil rank of $ E(K) $.

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Oriented trees in n-chromatic digraphs ★★★

Author(s): Burr

Conjecture   Every digraph with chromatic number at least $ 2k-2 $ contains every oriented tree of order $ k $ as a subdigraph.

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Laplacian Degrees of a Graph ★★

Author(s): Guo

Conjecture   If $ G $ is a connected graph on $ n $ vertices, then $ c_k(G) \ge d_k(G) $ for $ k = 1, 2, \dots, n-1 $.

Keywords: degree sequence; Laplacian matrix

3-Decomposition Conjecture ★★

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3-Decomposition Conjecture

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Candy Crush Saga Free Golds Lives Cheats 2024-2024 Edition v9 (Verified) ★★

Author(s):

Candy Crush Saga Free Golds Lives Cheats 2024-2024 Edition v9 (Verified)

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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

The Sims Mobile Cheats Generator Working Android Ios 2024 Cheats Generator (Newly Discovered) ★★

Author(s):

The Sims Mobile Cheats Generator Working Android Ios 2024 Cheats Generator (Newly Discovered)

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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

Domination in cubic graphs ★★

Author(s): Reed

Problem   Does every 3-connected cubic graph $ G $ satisfy $ \gamma(G) \le \lceil |G|/3 \rceil $ ?

Keywords: cubic graph; domination

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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Dragon Ball Legends Cheats Generator (Ios Android) ★★

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Dragon Ball Legends Cheats Generator (Ios Android)

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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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War Dragons Rubies Cheats Generator 2024 (improved version) ★★

Author(s):

War Dragons Rubies Cheats Generator 2024 (improved version)

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Dice Dreams Cheats Generator Free Unlimited Cheats Generator (LATEST) ★★

Author(s):

Dice Dreams Cheats Generator Free Unlimited Cheats Generator (LATEST)

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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

V-Bucks Generator Unlimited IOS Android No Survey 2024 (FREE METHOD) ★★

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V-Bucks Generator Unlimited IOS Android No Survey 2024 (FREE METHOD)

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Saturated $k$-Sperner Systems of Minimum Size ★★

Author(s): Morrison; Noel; Scott

Question   Does there exist a constant $ c>1/2 $ and a function $ n_0(k) $ such that if $ |X|\geq n_0(k) $, then every saturated $ k $-Sperner system $ \mathcal{F}\subseteq \mathcal{P}(X) $ has cardinality at least $ 2^{(1+o(1))ck} $?

Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system

Family Island Cheats Generator 2024 No Human Verification (Real) ★★

Author(s):

Family Island Cheats Generator 2024 No Human Verification (Real)

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What is the largest graph of positive curvature?

Author(s): DeVos; Mohar

Problem   What is the largest connected planar graph of minimum degree 3 which has everywhere positive combinatorial curvature, but is not a prism or antiprism?

Keywords: curvature; planar graph

The Ultimate Guide to Simpsons Tapped Out Cheats: Unlocking Donuts and Cash ★★

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Conjecture  

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