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Seagull problem ★★

Author(s):

Seagull problem

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Forcing a $K_6$-minor ★★

Author(s): Barát ; Joret; Wood

Conjecture   Every graph with minimum degree at least 7 contains a $ K_6 $-minor.
Conjecture   Every 7-connected graph contains a $ K_6 $-minor.

Keywords: connectivity; graph minors

Ádám's Conjecture ★★★

Author(s): Ádám

Conjecture   Every digraph with at least one directed cycle has an arc whose reversal reduces the number of directed cycles.

Keywords:

Atomicity of the poset of completary multifuncoids ★★

Author(s): Porton

Conjecture   The poset of completary multifuncoids of the form $ (\mathscr{P}\mho)^n $ is for every sets $ \mho $ and $ n $:
    \item atomic; \item atomistic.

See below for definition of all concepts and symbols used to in this conjecture.

Refer to this Web site for the theory which I now attempt to generalize.

Keywords: multifuncoid

Brawlhalla Cheats Generator 2024 No Human Veryfication (codes) ★★

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Brawlhalla Cheats Generator 2024 No Human Veryfication (codes)

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Brawlhalla Cheats Generator 2024 (safe and working) ★★

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Brawlhalla Cheats Generator 2024 (safe and working)

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Slice-ribbon problem ★★★★

Author(s): Fox

Conjecture   Given a knot in $ S^3 $ which is slice, is it a ribbon knot?

Keywords: cobordism; knot; ribbon; slice

Fishdom Cheats Generator without verification (Free) ★★

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Fishdom Cheats Generator without verification (Free)

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Lords Mobile Working Cheats Gems Coins Generator (NEW AND FREE) ★★

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Lords Mobile Working Cheats Gems Coins Generator (NEW AND FREE)

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P vs. PSPACE ★★★

Author(s): Folklore

Problem   Is there a problem that can be computed by a Turing machine in polynomial space and unbounded time but not in polynomial time? More formally, does P = PSPACE?

Keywords: P; PSPACE; separation; unconditional

Toon Blast Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra) ★★

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Toon Blast Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra)

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Bases of many weights ★★★

Author(s): Schrijver; Seymour

Let $ G $ be an (additive) abelian group, and for every $ S \subseteq G $ let $ {\mathit stab}(S) = \{ g \in G : g + S = S \} $.

Conjecture   Let $ M $ be a matroid on $ E $, let $ w : E \rightarrow G $ be a map, put $ S = \{ \sum_{b \in B} w(b) : B \mbox{ is a base} \} $ and $ H = {\mathit stab}(S) $. Then $$|S| \ge |H| \left( 1 - rk(M) + \sum_{Q \in G/H} rk(w^{-1}(Q)) \right).$$

Keywords: matroid; sumset; zero sum

3-Decomposition Conjecture ★★★

Author(s): Arthur; Hoffmann-Ostenhof

Conjecture   (3-Decomposition Conjecture) Every connected cubic graph $ G $ has a decomposition into a spanning tree, a family of cycles and a matching.

Keywords: cubic graph

Erdős–Straus conjecture ★★

Author(s): Erdos; Straus

Conjecture  

For all $ n > 2 $, there exist positive integers $ x $, $ y $, $ z $ such that $$1/x + 1/y + 1/z = 4/n$$.

Keywords: Egyptian fraction

Roller Coaster permutations ★★★

Author(s): Ahmed; Snevily

Let $ S_n $ denote the set of all permutations of $ [n]=\set{1,2,\ldots,n} $. Let $ i(\pi) $ and $ d(\pi) $ denote respectively the number of increasing and the number of decreasing sequences of contiguous numbers in $ \pi $. Let $ X(\pi) $ denote the set of subsequences of $ \pi $ with length at least three. Let $ t(\pi) $ denote $ \sum_{\tau\in X(\pi)}(i(\tau)+d(\tau)) $.

A permutation $ \pi\in S_n $ is called a Roller Coaster permutation if $ t(\pi)=\max_{\tau\in S_n}t(\tau) $. Let $ RC(n) $ be the set of all Roller Coaster permutations in $ S_n $.

Conjecture   For $ n\geq 3 $,
    \item If $ n=2k $, then $ |RC(n)|=4 $. \item If $ n=2k+1 $, then $ |RC(n)|=2^j $ with $ j\leq k+1 $.
Conjecture  (Odd Sum conjecture)   Given $ \pi\in RC(n) $,
    \item If $ n=2k+1 $, then $ \pi_j+\pi_{n-j+1} $ is odd for $ 1\leq j\leq k $. \item If $ n=2k $, then $ \pi_j + \pi_{n-j+1} = 2k+1 $ for all $ 1\leq j\leq k $.

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Characterizing (aleph_0,aleph_1)-graphs ★★★

Author(s): Diestel; Leader

Call a graph an $ (\aleph_0,\aleph_1) $-graph if it has a bipartition $ (A,B) $ so that every vertex in $ A $ has degree $ \aleph_0 $ and every vertex in $ B $ has degree $ \aleph_1 $.

Problem   Characterize the $ (\aleph_0,\aleph_1) $-graphs.

Keywords: binary tree; infinite graph; normal spanning tree; set theory

Dragon Ball Z Dokkan Battle Cheats Generator 2024 (LEGIT) ★★

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Dragon Ball Z Dokkan Battle Cheats Generator 2024 (LEGIT)

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Warframe Cheats Generator (iOS Android 2024) ★★

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Warframe Cheats Generator (iOS Android 2024)

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Golf Battle Cheats Generator (Ios Android) ★★

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Golf Battle Cheats Generator (Ios Android)

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The three 4-flows conjecture ★★

Author(s): DeVos

Conjecture   For every graph $ G $ with no bridge, there exist three disjoint sets $ A_1,A_2,A_3 \subseteq E(G) $ with $ A_1 \cup A_2 \cup A_3 = E(G) $ so that $ G \setminus A_i $ has a nowhere-zero 4-flow for $ 1 \le i \le 3 $.

Keywords: nowhere-zero flow

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

Author(s):

War Dragons Rubies Cheats Generator 2024 (improved version)

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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

Choosability of Graph Powers ★★

Author(s): Noel

Question  (Noel, 2013)   Does there exist a function $ f(k)=o(k^2) $ such that for every graph $ G $, \[\text{ch}\left(G^2\right)\leq f\left(\chi\left(G^2\right)\right)?\]

Keywords: choosability; chromatic number; list coloring; square of a graph

Hamiltonian paths and cycles in vertex transitive graphs ★★★

Author(s): Lovasz

Problem   Does every connected vertex-transitive graph have a Hamiltonian path?

Keywords: cycle; hamiltonian; path; vertex-transitive

Average diameter of a bounded cell of a simple arrangement ★★

Author(s): Deza; Terlaky; Zinchenko

Conjecture   The average diameter of a bounded cell of a simple arrangement defined by $ n $ hyperplanes in dimension $ d $ is not greater than $ d $.

Keywords: arrangement; diameter; polytope

Fortnite Working Generator V-Bucks Generator (NEW AND FREE) ★★

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Fortnite Working Generator V-Bucks Generator (NEW AND FREE)

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"Working Cheats" Sims FreePlay Simoleons Life Points and Social Points Generator No Human Verification 2024 ★★

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"Working Cheats" Sims FreePlay Simoleons Life Points and Social Points Generator No Human Verification 2024

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World Of Tanks Blitz Gold Credits Cheats 2024 (re-designed) ★★

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World Of Tanks Blitz Gold Credits Cheats 2024 (re-designed)

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Melnikov's valency-variety problem

Author(s): Melnikov

Problem   The valency-variety $ w(G) $ of a graph $ G $ is the number of different degrees in $ G $. Is the chromatic number of any graph $ G $ with at least two vertices greater than $$\ceil{ \frac{\floor{w(G)/2}}{|V(G)| - w(G)} } ~ ?$$

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Free Jurassic Park Builder Cheats Generator Pro Apk (2024) ★★

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Free Jurassic Park Builder Cheats Generator Pro Apk (2024)

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

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Free Clash of Clans Cheats Gems Generator 2023-2024

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Good Edge Labelings ★★

Author(s): Araújo; Cohen; Giroire; Havet

Question   What is the maximum edge density of a graph which has a good edge labeling?

We say that a graph is good-edge-labeling critical, if it has no good edge labeling, but every proper subgraph has a good edge labeling.

Conjecture   For every $ c<4 $, there is only a finite number of good-edge-labeling critical graphs with average degree less than $ c $.

Keywords: good edge labeling, edge labeling

Infinite uniquely hamiltonian graphs ★★

Author(s): Mohar

Problem   Are there any uniquely hamiltonian locally finite 1-ended graphs which are regular of degree $ r > 2 $?

Keywords: hamiltonian; infinite graph; uniquely hamiltonian

Weak saturation of the cube in the clique

Author(s): Morrison; Noel

Problem  

Determine $ \text{wsat}(K_n,Q_3) $.

Keywords: bootstrap percolation; hypercube; Weak saturation

Hungry Shark Evolution Cheats Generator 2024 Cheats Generator Tested On Android Ios (WORKING TIPS) ★★

Author(s):

Hungry Shark Evolution Cheats Generator 2024 Cheats Generator Tested On Android Ios (WORKING TIPS)

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Beneš Conjecture (graph-theoretic form) ★★★

Author(s): Beneš

Problem  ($ \dag $)   Find a sufficient condition for a straight $ \ell $-stage graph to be rearrangeable. In particular, what about a straight uniform graph?
Conjecture  ($ \diamond $)   Let $ L $ be a simple regular ordered $ 2 $-stage graph. Suppose that the graph $ L^m $ is externally connected, for some $ m\ge1 $. Then the graph $ L^{2m} $ is rearrangeable.

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MovieStarPlanet Generator Cheats 2024 (WORKING IN 5 SECOND) ★★

Author(s):

MovieStarPlanet Generator Cheats 2024 (WORKING IN 5 SECOND)

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Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator (New 2024) ★★

Author(s):

Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator (New 2024)

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A nowhere-zero point in a linear mapping ★★★

Author(s): Jaeger

Conjecture   If $ {\mathbb F} $ is a finite field with at least 4 elements and $ A $ is an invertible $ n \times n $ matrix with entries in $ {\mathbb F} $, then there are column vectors $ x,y \in {\mathbb F}^n $ which have no coordinates equal to zero such that $ Ax=y $.

Keywords: invertible; nowhere-zero flow

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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Gardenscapes Cheats Generator 2024 for Android iOS (updated Generator) ★★

Author(s):

Gardenscapes Cheats Generator 2024 for Android iOS (updated Generator)

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

Author(s):

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

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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

The 3n+1 conjecture ★★★

Author(s): Collatz

Conjecture   Let $ f(n) = 3n+1 $ if $ n $ is odd and $ \frac{n}{2} $ if $ n $ is even. Let $ f(1) = 1 $. Assume we start with some number $ n $ and repeatedly take the $ f $ of the current number. Prove that no matter what the initial number is we eventually reach $ 1 $.

Keywords: integer sequence

KPZ Universality Conjecture ★★★

Author(s):

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

Keywords: KPZ equation, central limit theorem

Alexa's Conjecture on Primality ★★

Author(s): Alexa

Definition   Let $ r_i $ be the unique integer (with respect to a fixed $ p\in\mathbb{N} $) such that

$$(2i+1)^{p-1} \equiv r_i \pmod p ~~\text{ and } ~ 0 \le r_i < p. $$

Conjecture   A natural number $ p \ge 8 $ is a prime iff $$ \displaystyle \sum_{i=1}^{\left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor} r_i = \left \lfloor \frac{\sqrt[3]p}{2} \right \rfloor $$

Keywords: primality

Graph product of multifuncoids ★★

Author(s): Porton

Conjecture   Let $ F $ is a family of multifuncoids such that each $ F_i $ is of the form $ \lambda j \in N \left( i \right) : \mathfrak{F} \left( U_j \right) $ where $ N \left( i \right) $ is an index set for every $ i $ and $ U_j $ is a set for every $ j $. Let every $ F_i = E^{\ast} f_i $ for some multifuncoid $ f_i $ of the form $ \lambda j \in N \left( i \right) : \mathfrak{P} \left( U_j \right) $ regarding the filtrator $ \left( \prod_{j \in N \left( i \right)} \mathfrak{F} \left( U_j \right) ; \prod_{j \in N \left( i \right)} \mathfrak{P} \left( U_j \right) \right) $. Let $ H $ is a graph-composition of $ F $ (regarding some partition $ G $ and external set $ Z $). Then there exist a multifuncoid $ h $ of the form $ \lambda j \in Z : \mathfrak{P} \left( U_j \right) $ such that $ H = E^{\ast} h $ regarding the filtrator $ \left( \prod_{j \in Z} \mathfrak{F} \left( U_j \right) ; \prod_{j \in Z} \mathfrak{P} \left( U_j \right) \right) $.

Keywords: graph-product; multifuncoid

Apex Legends Coins Cheats 2024 (Ios Android) ★★

Author(s):

Apex Legends Coins Cheats 2024 (Ios Android)

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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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