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Geodesic cycles and Tutte's Theorem ★★

Author(s): Georgakopoulos; Sprüssel

Problem   If $ G $ is a $ 3 $-connected finite graph, is there an assignment of lengths $ \ell: E(G) \to \mathb R^+ $ to the edges of $ G $, such that every $ \ell $-geodesic cycle is peripheral?

Keywords: cycle space; geodesic cycles; peripheral cycles

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

Minimum number of arc-disjoint transitive subtournaments of order 3 in a tournament ★★

Author(s): Yuster

Conjecture   If $ T $ is a tournament of order $ n $, then it contains $ \left \lceil n(n-1)/6 - n/3\right\rceil $ arc-disjoint transitive subtournaments of order 3.

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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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Crossing numbers and coloring ★★★

Author(s): Albertson

We let $ cr(G) $ denote the crossing number of a graph $ G $.

Conjecture   Every graph $ G $ with $ \chi(G) \ge t $ satisfies $ cr(G) \ge cr(K_t) $.

Keywords: coloring; complete graph; crossing number

3 is a primitive root modulo primes of the form 16 q^4 + 1, where q>3 is prime ★★

Author(s):

Conjecture   $ 3~ $ is a primitive root modulo $ ~p $ for all primes $ ~p=16\cdot q^4+1 $, where $ ~q>3 $ is prime.

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

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

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Large acyclic induced subdigraph in a planar oriented graph. ★★

Author(s): Harutyunyan

Conjecture   Every planar oriented graph $ D $ has an acyclic induced subdigraph of order at least $ \frac{3}{5} |V(D)| $.

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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

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

Author(s):

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

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

Author(s):

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

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Large induced forest in a planar graph. ★★

Author(s): Abertson; Berman

Conjecture   Every planar graph on $ n $ verices has an induced forest with at least $ n/2 $ vertices.

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Free Hollywood Story Free Diamonds Gems Cheats 2024 (Safe) ★★

Author(s):

Free Hollywood Story Free Diamonds Gems Cheats 2024 (Safe)

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Fishing Clash Cheats Generator 2024 No Verification Android iOS (new method) ★★

Author(s):

Fishing Clash Cheats Generator 2024 No Verification Android iOS (new method)

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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

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

Triangle free strongly regular graphs ★★★

Author(s):

Problem   Is there an eighth triangle free strongly regular graph?

Keywords: strongly regular; triangle free

Linear Hypergraphs with Dimension 3 ★★

Author(s): de Fraysseix; Ossona de Mendez; Rosenstiehl

Conjecture   Any linear hypergraph with incidence poset of dimension at most 3 is the intersection hypergraph of a family of triangles and segments in the plane.

Keywords: Hypergraphs

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

Author(s):

Easy! Unlimited Dragon City Cheats Generator codes (GLITCH)

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The Sims Mobile Cheats Generator 2024 for Android iOS (UPDATED Generator) ★★

Author(s):

The Sims Mobile Cheats Generator 2024 for Android iOS (UPDATED Generator)

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SimCity BuildIt Cheats Generator 2024 (No Human Verification) ★★

Author(s):

SimCity BuildIt Cheats Generator 2024 (No Human Verification)

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

Author(s):

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

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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

Codes Free Royal Match Coins Cheats 2024 No Human Veryfication!!! ★★

Author(s):

Codes Free Royal Match Coins Cheats 2024 No Human Veryfication!!!

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Every metamonovalued reloid is monovalued ★★

Author(s): Porton

Conjecture   Every metamonovalued reloid is monovalued.

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Free Warframe Platinum Cheats Pro Apk 2024 (Android Ios) ★★

Author(s):

Free Warframe Platinum Cheats Pro Apk 2024 (Android Ios)

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Invariant subspace problem ★★★

Author(s):

Problem   Does every bounded linear operator on an infinite-dimensional separable Hilbert space have a non-trivial closed invariant subspace?

Keywords: subspace

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

World of Warships Cheats Generator Fully Works No Survey Cheats Generator (2024) ★★

Author(s):

World of Warships Cheats Generator Fully Works No Survey Cheats Generator (2024)

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Sums of independent random variables with unbounded variance ★★

Author(s): Feige

Conjecture   If $ X_1, \dotsc, X_n \geq 0 $ are independent random variables with $ \mathbb{E}[X_i] \leq \mu $, then $$\mathrm{Pr} \left( \sum X_i - \mathbb{E} \left[ \sum X_i \right ] < \delta \mu \right) \geq \min \left ( (1 + \delta)^{-1} \delta, e^{-1} \right).$$

Keywords: Inequality; Probability Theory; randomness in TCS

Singmaster's conjecture ★★

Author(s): Singmaster

Conjecture   There is a finite upper bound on the multiplicities of entries in Pascal's triangle, other than the number $ 1 $.

The number $ 2 $ appears once in Pascal's triangle, $ 3 $ appears twice, $ 6 $ appears three times, and $ 10 $ appears $ 4 $ times. There are infinite families of numbers known to appear $ 6 $ times. The only number known to appear $ 8 $ times is $ 3003 $. It is not known whether any number appears more than $ 8 $ times. The conjectured upper bound could be $ 8 $; Singmaster thought it might be $ 10 $ or $ 12 $. See Singmaster's conjecture.

Keywords: Pascal's triangle

Quartic rationally derived polynomials ★★★

Author(s): Buchholz; MacDougall

Call a polynomial $ p \in {\mathbb Q}[x] $ rationally derived if all roots of $ p $ and the nonzero derivatives of $ p $ are rational.

Conjecture   There does not exist a quartic rationally derived polynomial $ p \in {\mathbb Q}[x] $ with four distinct roots.

Keywords: derivative; diophantine; elliptic; polynomial

Decomposing k-arc-strong tournament into k spanning strong digraphs ★★

Author(s): Bang-Jensen; Yeo

Conjecture   Every k-arc-strong tournament decomposes into k spanning strong digraphs.

Keywords:

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

Author(s):

Match Masters Coins Cheats 2024 Update (FREE!!)

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Several ways to apply a (multivalued) multiargument function to a family of filters ★★★

Author(s): Porton

Problem   Let $ \mathcal{X} $ be an indexed family of filters on sets. Which of the below items are always pairwise equal?

1. The funcoid corresponding to this function (considered as a single argument function on indexed families) applied to the reloidal product of filters $ \mathcal{X} $.

2. The funcoid corresponding to this function (considered as a single argument function on indexed families) applied to the starred reloidal product of filters $ \mathcal{X} $.

3. $ \bigcap_{F\in\operatorname{up}^{\mathrm{FCD}}\prod^{\mathrm{Strd}}\mathcal{X}}\langle f \rangle F $.

Keywords: funcoid; function; multifuncoid; staroid

Divisibility of central binomial coefficients ★★

Author(s): Graham

Problem  (1)   Prove that there exist infinitely many positive integers $ n $ such that $$\gcd({2n\choose n}, 3\cdot 5\cdot 7) = 1.$$
Problem  (2)   Prove that there exists only a finite number of positive integers $ n $ such that $$\gcd({2n\choose n}, 3\cdot 5\cdot 7\cdot 11) = 1.$$

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Mastering Subway Surfers: The Ultimate Guide to Cheats, Hacks, and Generators ★★

Author(s):

Mastering Subway Surfers: The Ultimate Guide to Cheats, Hacks, and Generators

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Cooking Fever Cheats Generator Unlimited Cheats Generator (No Human Verification) ★★

Author(s):

Cooking Fever Cheats Generator Unlimited Cheats Generator (No Human Verification)

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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

Geometry Dash Gold Coins Stars Cheats 2024 Update (FREE!!) ★★

Author(s):

Geometry Dash Gold Coins Stars Cheats 2024 Update (FREE!!)

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3-Edge-Coloring Conjecture ★★★

Author(s): Arthur; Hoffmann-Ostenhof

Conjecture   Suppose $ G $ with $ |V(G)|>2 $ is a connected cubic graph admitting a $ 3 $-edge coloring. Then there is an edge $ e \in E(G) $ such that the cubic graph homeomorphic to $ G-e $ has a $ 3 $-edge coloring.

Keywords: 3-edge coloring; 4-flow; removable edge

Double-critical graph conjecture ★★

Author(s): Erdos; Lovasz

A connected simple graph $ G $ is called double-critical, if removing any pair of adjacent vertexes lowers the chromatic number by two.

Conjecture   $ K_n $ is the only $ n $-chromatic double-critical graph

Keywords: coloring; complete graph

Dragon Ball Legends Cheats Generator (Ios Android) ★★

Author(s):

Dragon Ball Legends Cheats Generator (Ios Android)

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Strong 5-cycle double cover conjecture ★★★

Author(s): Arthur; Hoffmann-Ostenhof

Conjecture   Let $ C $ be a circuit in a bridgeless cubic graph $ G $. Then there is a five cycle double cover of $ G $ such that $ C $ is a subgraph of one of these five cycles.

Keywords: cycle cover

World Of Tanks Blitz Gold Credits Cheats Generator 2024 (improved version) ★★

Author(s):

World Of Tanks Blitz Gold Credits Cheats Generator 2024 (improved version)

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A gold-grabbing game ★★

Author(s): Rosenfeld

Setup Fix a tree $ T $ and for every vertex $ v \in V(T) $ a non-negative integer $ g(v) $ which we think of as the amount of gold at $ v $.

2-Player game Players alternate turns. On each turn, a player chooses a leaf vertex $ v $ of the tree, takes the gold at this vertex, and then deletes $ v $. The game ends when the tree is empty, and the winner is the player who has accumulated the most gold.

Problem   Find optimal strategies for the players.

Keywords: game; tree

eFootball 2023 Cheats Generator IOS Android No Verification 2024 (NEW STRATEGY) ★★

Author(s):

eFootball 2023 Cheats Generator IOS Android No Verification 2024 (NEW STRATEGY)

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Infinite distributivity of meet over join for a principal funcoid ★★

Author(s): Porton

Conjecture   $ f \sqcap \bigsqcup S = \bigsqcup \langle f \sqcap \rangle^{\ast} S $ for principal funcoid $ f $ and a set $ S $ of funcoids of appropriate sources and destinations.

Keywords: distributivity; principal funcoid

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

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.

Keywords: