Random

"New Cheats" Subway Surfers Coins Keys Cheats Free 2024 ★★

Author(s):

"New Cheats" Subway Surfers Coins Keys Cheats Free 2024

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Cores of strongly regular graphs ★★★

Author(s): Cameron; Kazanidis

Question   Does every strongly regular graph have either itself or a complete graph as a core?

Keywords: core; strongly regular

Gta 5 Cheats Generator No Human Verification (Ios Android) ★★

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Gta 5 Cheats Generator No Human Verification (Ios Android)

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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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Apex Legends Coins Cheats 2024 (rejuvenated cheats) ★★

Author(s):

Apex Legends Coins Cheats 2024 (rejuvenated cheats)

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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

Unions of triangle free graphs ★★★

Author(s): Erdos; Hajnal

Problem   Does there exist a graph with no subgraph isomorphic to $ K_4 $ which cannot be expressed as a union of $ \aleph_0 $ triangle free graphs?

Keywords: forbidden subgraph; infinite graph; triangle free

Cookie Run Kingdom Cheats Generator Android Ios 2024 Cheats Generator (free) ★★

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Cookie Run Kingdom Cheats Generator Android Ios 2024 Cheats Generator (free)

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eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (Reedem Today) ★★

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eFootball 2023 Cheats Generator Unlimited IOS Android No Survey 2024 (Reedem Today)

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Match Masters Free Coins Cheats 2024 (LEGIT) ★★

Author(s):

Match Masters Free Coins Cheats 2024 (LEGIT)

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Tarski's exponential function problem ★★

Author(s): Tarski

Conjecture   Is the theory of the real numbers with the exponential function decidable?

Keywords: Decidability

War Dragons Rubies Cheats 2024 (rejuvenated cheats) ★★

Author(s):

War Dragons Rubies Cheats 2024 (rejuvenated cheats)

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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.

Keywords:

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

Are vertex minor closed classes chi-bounded? ★★

Author(s): Geelen

Question   Is every proper vertex-minor closed class of graphs chi-bounded?

Keywords: chi-bounded; circle graph; coloring; vertex minor

Open problem ★★

Author(s):

Open problem

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Matchings extend to Hamiltonian cycles in hypercubes ★★

Author(s): Ruskey; Savage

Question   Does every matching of hypercube extend to a Hamiltonian cycle?

Keywords: Hamiltonian cycle; hypercube; matching

Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator IOS Android 2024 (get codes) ★★

Author(s):

Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator IOS Android 2024 (get codes)

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Hamilton cycle in small d-diregular graphs ★★

Author(s): Jackson

An directed graph is $ k $-diregular if every vertex has indegree and outdegree at least $ k $.

Conjecture   For $ d >2 $, every $ d $-diregular oriented graph on at most $ 4d+1 $ vertices has a Hamilton cycle.

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Acyclic edge-colouring ★★

Author(s): Fiamcik

Conjecture   Every simple graph with maximum degree $ \Delta $ has a proper $ (\Delta+2) $-edge-colouring so that every cycle contains edges of at least three distinct colours.

Keywords: edge-coloring

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

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

Family Island Cheats Generator 2024 Free No Verification (New.updated) ★★

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Family Island Cheats Generator 2024 Free No Verification (New.updated)

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Cooking Fever Cheats Generator Android Ios No Survey 2024 (NEW) ★★

Author(s):

Cooking Fever Cheats Generator Android Ios No Survey 2024 (NEW)

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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

A diagram about funcoids and reloids ★★

Author(s): Porton

Define for posets with order $ \sqsubseteq $:

  1. $ \Phi_{\ast} f = \lambda b \in \mathfrak{B}: \bigcup \{ x \in \mathfrak{A} \mid f x \sqsubseteq b \} $;
  2. $ \Phi^{\ast} f = \lambda b \in \mathfrak{A}: \bigcap \{ x \in \mathfrak{B} \mid f x \sqsupseteq b \} $.

Note that the above is a generalization of monotone Galois connections (with $ \max $ and $ \min $ replaced with suprema and infima).

Then we have the following diagram:

What is at the node "other" in the diagram is unknown.

Conjecture   "Other" is $ \lambda f\in\mathsf{FCD}: \top $.
Question   What repeated applying of $ \Phi_{\ast} $ and $ \Phi^{\ast} $ to "other" leads to? Particularly, does repeated applying $ \Phi_{\ast} $ and/or $ \Phi^{\ast} $ to the node "other" lead to finite or infinite sets?

Keywords: Galois connections

Vertex Cover Integrality Gap ★★

Author(s): Atserias

Conjecture   For every $ \varepsilon > 0 $ there is $ \delta > 0 $ such that, for every large $ n $, there are $ n $-vertex graphs $ G $ and $ H $ such that $ G \equiv_{\delta n}^{\mathrm{C}} H $ and $ \mathrm{vc}(G) \ge (2 - \varepsilon) \cdot \mathrm{vc}(H) $.

Keywords: counting quantifiers; FMT12-LesHouches

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

3-flow conjecture ★★★

Author(s): Tutte

Conjecture   Every 4-edge-connected graph has a nowhere-zero 3-flow.

Keywords: nowhere-zero flow

Primitive pythagorean n-tuple tree ★★

Author(s):

Conjecture   Find linear transformation construction of primitive pythagorean n-tuple tree!

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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

Genshin Impact Cheats Generator Cheats Generator 2023-2024 (Free!!) ★★

Author(s):

Genshin Impact Cheats Generator Cheats Generator 2023-2024 (Free!!)

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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

Cycles in Graphs of Large Chromatic Number ★★

Author(s): Brewster; McGuinness; Moore; Noel

Conjecture   If $ \chi(G)>k $, then $ G $ contains at least $ \frac{(k+1)(k-1)!}{2} $ cycles of length $ 0\bmod k $.

Keywords: chromatic number; cycles

Every prism over a 3-connected planar graph is hamiltonian. ★★

Author(s): Kaiser; Král; Rosenfeld; Ryjácek; Voss

Conjecture   If $ G $ is a $ 3 $-connected planar graph, then $ G\square K_2 $ has a Hamilton cycle.

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

Author(s):

Working Apex Legends Cheats Online Coins Generator (No Survey)

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Which compact boundaryless 3-manifolds embed smoothly in the 4-sphere? ★★★

Author(s): Kirby

Problem   Determine a computable set of invariants that allow one to determine, given a compact boundaryless 3-manifold, whether or not it embeds smoothly in the 4-sphere. This should include a constructive procedure to find an embedding if the manifold is embeddable.

Keywords: 3-manifold; 4-sphere; embedding

Subset-sums equality (pigeonhole version) ★★★

Author(s):

Problem   Let $ a_1,a_2,\ldots,a_n $ be natural numbers with $ \sum_{i=1}^n a_i < 2^n - 1 $. It follows from the pigeon-hole principle that there exist distinct subsets $ I,J \subseteq \{1,\ldots,n\} $ with $ \sum_{i \in I} a_i = \sum_{j \in J} a_j $. Is it possible to find such a pair $ I,J $ in polynomial time?

Keywords: polynomial algorithm; search problem

Legal* Free Coin Master Cheats Spins Coins Generator No Human Verification 2024 ★★

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Legal* Free Coin Master Cheats Spins Coins Generator No Human Verification 2024

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Simultaneous partition of hypergraphs ★★

Author(s): Kühn; Osthus

Problem   Let $ H_1 $ and $ H_2 $ be two $ r $-uniform hypergraph on the same vertex set $ V $. Does there always exist a partition of $ V $ into $ r $ classes $ V_1, \dots , V_r $ such that for both $ i=1,2 $, at least $ r!m_i/r^r -o(m_i) $ hyperedges of $ H_i $ meet each of the classes $ V_1, \dots , V_r $?

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Fasted Way! For Free Brawlhalla Cheats Generator Working 2024 Android Ios ★★

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Fasted Way! For Free Brawlhalla Cheats Generator Working 2024 Android Ios

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

Author(s):

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

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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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Free Clash of Clans Cheats Gems Generator 2023-2024 ★★

Author(s):

Free Clash of Clans Cheats Gems Generator 2023-2024

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Distribution and upper bound of mimic numbers ★★

Author(s): Bhattacharyya

Problem  

Let the notation $ a|b $ denote ''$ a $ divides $ b $''. The mimic function in number theory is defined as follows [1].

Definition   For any positive integer $ \mathcal{N} = \sum_{i=0}^{n}\mathcal{X}_{i}\mathcal{M}^{i} $ divisible by $ \mathcal{D} $, the mimic function, $ f(\mathcal{D} | \mathcal{N}) $, is given by,

$$ f(\mathcal{D} | \mathcal{N}) = \sum_{i=0}^{n}\mathcal{X}_{i}(\mathcal{M}-\mathcal{D})^{i} $$

By using this definition of mimic function, the mimic number of any non-prime integer is defined as follows [1].

Definition   The number $ m $ is defined to be the mimic number of any positive integer $ \mathcal{N} = \sum_{i=0}^{n}\mathcal{X}_{i}\mathcal{M}^{i} $, with respect to $ \mathcal{D} $, for the minimum value of which $ f^{m}(\mathcal{D} | \mathcal{N}) = \mathcal{D} $.

Given these two definitions and a positive integer $ \mathcal{D} $, find the distribution of mimic numbers of those numbers divisible by $ \mathcal{D} $.

Again, find whether there is an upper bound of mimic numbers for a set of numbers divisible by any fixed positive integer $ \mathcal{D} $.

Keywords: Divisibility; mimic function; mimic number

SimCity BuildIt Cheats Generator Free 2024 No Human Verification (New Update) ★★

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SimCity BuildIt Cheats Generator Free 2024 No Human Verification (New Update)

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

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

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"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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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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