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

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Hungry Shark Evolution Cheats Generator 2024 Working (Generator)

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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

Arc-disjoint strongly connected spanning subdigraphs ★★

Author(s): Bang-Jensen; Yeo

Conjecture   There exists an ineteger $ k $ so that every $ k $-arc-connected digraph contains a pair of arc-disjoint strongly connected spanning subdigraphs?

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The intersection of two perfect matchings ★★

Author(s): Macajova; Skoviera

Conjecture   Every bridgeless cubic graph has two perfect matchings $ M_1 $, $ M_2 $ so that $ M_1 \cap M_2 $ does not contain an odd edge-cut.

Keywords: cubic; nowhere-zero flow; perfect matching

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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Cookie Run Kingdom Cheats Generator Unlimited Cheats Generator (New 2024) ★★

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Cookie Run Kingdom Cheats Generator Unlimited Cheats Generator (New 2024)

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Real Racing 3 Cheats Generator Working 2024 (Real Racing 3 Generator) ★★

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Real Racing 3 Cheats Generator Working 2024 (Real Racing 3 Generator)

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Dragon Ball Legends Free Cheats Generator 999,999k Free 2024 (Free Generator) ★★

Author(s):

Dragon Ball Legends Free Cheats Generator 999,999k Free 2024 (Free Generator)

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Sub-atomic product of funcoids is a categorical product ★★

Author(s):

Conjecture   In the category of continuous funcoids (defined similarly to the category of topological spaces) the following is a direct categorical product:
    \item Product morphism is defined similarly to the category of topological spaces. \item Product object is the sub-atomic product. \item Projections are sub-atomic projections.

See details, exact definitions, and attempted proofs here.

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3-Decomposition Conjecture ★★

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3-Decomposition Conjecture

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Covering a square with unit squares ★★

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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.

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Question about 'solving' something ★★

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Conjecture  

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Gta 5 Cheats Generator 2024 No Human Verification (Brand New) ★★

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Gta 5 Cheats Generator 2024 No Human Verification (Brand New)

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Codes Free Star Stable Star Coins Jorvik Coins Cheats 2024 No Human Veryfication!!! ★★

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Codes Free Star Stable Star Coins Jorvik Coins Cheats 2024 No Human Veryfication!!!

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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

PK XD Generator Cheats 2024 Generator Cheats Tested On Android Ios (WORKING TIPS) ★★

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PK XD Generator Cheats 2024 Generator Cheats Tested On Android Ios (WORKING TIPS)

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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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Extremal problem on the number of tree endomorphism ★★

Author(s): Zhicong Lin

Conjecture   An endomorphism of a graph is a mapping on the vertex set of the graph which preserves edges. Among all the $ n $ vertices' trees, the star with $ n $ vertices has the most endomorphisms, while the path with $ n $ vertices has the least endomorphisms.

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Monochromatic empty triangles ★★

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Monochromatic empty triangles

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Inscribed Square Problem ★★

Author(s): Toeplitz

Conjecture   Does every Jordan curve have 4 points on it which form the vertices of a square?

Keywords: simple closed curve; square

House Of Fun Cheats Generator (iOS Android 2024) ★★

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House Of Fun Cheats Generator (iOS Android 2024)

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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

Cooking Fever Cheats Generator Free 2024 in 5 minutes (New Cheats Generator Cooking Fever) ★★

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Cooking Fever Cheats Generator Free 2024 in 5 minutes (New Cheats Generator Cooking Fever)

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Hello ★★

Author(s):

Hello

http://www.openproblemgarden.org/op/hello

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Free Idle Miner Tycoon Cheats Generator No Human Verification No Survey (Unused) ★★

Author(s):

Free Idle Miner Tycoon Cheats Generator No Human Verification No Survey (Unused)

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Asymptotic Distribution of Form of Polyhedra ★★

Author(s): Rüdinger

Problem   Consider the set of all topologically inequivalent polyhedra with $ k $ edges. Define a form parameter for a polyhedron as $ \beta:= v/(k+2) $ where $ v $ is the number of vertices. What is the distribution of $ \beta $ for $ k \to \infty $?

Keywords: polyhedral graphs, distribution

Seymour's self-minor conjecture ★★★

Author(s): Seymour

Conjecture   Every infinite graph is a proper minor of itself.

Keywords: infinite graph; minor

Is there an algorithm to determine if a triangulated 4-manifold is combinatorially equivalent to the 4-sphere? ★★★

Author(s): Novikov

Problem   Is there an algorithm which takes as input a triangulated 4-manifold, and determines whether or not this manifold is combinatorially equivalent to the 4-sphere?

Keywords: 4-sphere; algorithm

Multicolour Erdős--Hajnal Conjecture ★★★

Author(s): Erdos; Hajnal

Conjecture   For every fixed $ k\geq2 $ and fixed colouring $ \chi $ of $ E(K_k) $ with $ m $ colours, there exists $ \varepsilon>0 $ such that every colouring of the edges of $ K_n $ contains either $ k $ vertices whose edges are coloured according to $ \chi $ or $ n^\varepsilon $ vertices whose edges are coloured with at most $ m-1 $ colours.

Keywords: ramsey theory

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

Shannon capacity of the seven-cycle ★★★

Author(s):

Problem   What is the Shannon capacity of $ C_7 $?

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The Ultimate Guide to Gardenscapes Cheats and Hacks: Boost Your Game in 2024 ★★

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Conjecture  

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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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Universal highly arc transitive digraphs ★★★

Author(s): Cameron; Praeger; Wormald

An alternating walk in a digraph is a walk $ v_0,e_1,v_1,\ldots,v_m $ so that the vertex $ v_i $ is either the head of both $ e_i $ and $ e_{i+1} $ or the tail of both $ e_i $ and $ e_{i+1} $ for every $ 1 \le i \le m-1 $. A digraph is universal if for every pair of edges $ e,f $, there is an alternating walk containing both $ e $ and $ f $

Question   Does there exist a locally finite highly arc transitive digraph which is universal?

Keywords: arc transitive; digraph

Turán's problem for hypergraphs ★★

Author(s): Turan

Conjecture   Every simple $ 3 $-uniform hypergraph on $ 3n $ vertices which contains no complete $ 3 $-uniform hypergraph on four vertices has at most $ \frac12 n^2(5n-3) $ hyperedges.
Conjecture   Every simple $ 3 $-uniform hypergraph on $ 2n $ vertices which contains no complete $ 3 $-uniform hypergraph on five vertices has at most $ n^2(n-1) $ hyperedges.

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End-Devouring Rays

Author(s): Georgakopoulos

Problem   Let $ G $ be a graph, $ \omega $ a countable end of $ G $, and $ K $ an infinite set of pairwise disjoint $ \omega $-rays in $ G $. Prove that there is a set $ K' $ of pairwise disjoint $ \omega $-rays that devours $ \omega $ such that the set of starting vertices of rays in $ K' $ equals the set of starting vertices of rays in $ K $.

Keywords: end; ray

A conjecture about direct product of funcoids ★★

Author(s): Porton

Conjecture   Let $ f_1 $ and $ f_2 $ are monovalued, entirely defined funcoids with $ \operatorname{Src}f_1=\operatorname{Src}f_2=A $. Then there exists a pointfree funcoid $ f_1 \times^{\left( D \right)} f_2 $ such that (for every filter $ x $ on $ A $) $$\left\langle f_1 \times^{\left( D \right)} f_2 \right\rangle x = \bigcup \left\{ \langle f_1\rangle X \times^{\mathsf{FCD}} \langle f_2\rangle X \hspace{1em} | \hspace{1em} X \in \mathrm{atoms}^{\mathfrak{A}} x \right\}.$$ (The join operation is taken on the lattice of filters with reversed order.)

A positive solution of this problem may open a way to prove that some funcoids-related categories are cartesian closed.

Keywords: category theory; general topology

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

Hamiltonicity of Cayley graphs ★★★

Author(s): Rapaport-Strasser

Question   Is every Cayley graph Hamiltonian?

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Exact colorings of graphs ★★

Author(s): Erickson

Conjecture   For $ c \geq m \geq 1 $, let $ P(c,m) $ be the statement that given any exact $ c $-coloring of the edges of a complete countably infinite graph (that is, a coloring with $ c $ colors all of which must be used at least once), there exists an exactly $ m $-colored countably infinite complete subgraph. Then $ P(c,m) $ is true if and only if $ m=1 $, $ m=2 $, or $ c=m $.

Keywords: graph coloring; ramsey theory

Bounding the chromatic number of triangle-free graphs with fixed maximum degree ★★

Author(s): Kostochka; Reed

Conjecture   A triangle-free graph with maximum degree $ \Delta $ has chromatic number at most $ \ceil{\frac{\Delta}{2}}+2 $.

Keywords: chromatic number; girth; maximum degree; triangle free

Dice Dreams Cheats Generator 2024 for Android iOS (REAL Generator) ★★

Author(s):

Dice Dreams Cheats Generator 2024 for Android iOS (REAL Generator)

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Wide partition conjecture ★★

Author(s): Chow; Taylor

Conjecture   An integer partition is wide if and only if it is Latin.

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Approximation Ratio for Maximum Edge Disjoint Paths problem ★★

Author(s): Bentz

Conjecture   Can the approximation ratio $ O(\sqrt{n}) $ be improved for the Maximum Edge Disjoint Paths problem (MaxEDP) in planar graphs or can an inapproximability result stronger than $ \mathcal{APX} $-hardness?

Keywords: approximation algorithms; Disjoint paths; planar graph; polynomial algorithm

Goldberg's conjecture ★★★

Author(s): Goldberg

The overfull parameter is defined as follows: \[ w(G) = \max_{H \subseteq G} \left\lceil \frac{ |E(H)| }{ \lfloor \tfrac{1}{2} |V(H)| \rfloor} \right\rceil. \]

Conjecture   Every graph $ G $ satisfies $ \chi'(G) \le \max\{ \Delta(G) + 1, w(G) \} $.

Keywords: edge-coloring; multigraph

Free DealDash Bids Cheats Bids Generator 2023-2024 ★★

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Free DealDash Bids Cheats Bids Generator 2023-2024

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Cycle double cover conjecture ★★★★

Author(s): Seymour; Szekeres

Conjecture   For every graph with no bridge, there is a list of cycles so that every edge is contained in exactly two.

Keywords: cover; cycle

Fishing Clash Cheats Generator Free 2024 (New) ★★

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Fishing Clash Cheats Generator Free 2024 (New)

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Free Matchington Mansion Cheats Stars Coins Generator 2024 (Legal) ★★

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Free Matchington Mansion Cheats Stars Coins Generator 2024 (Legal)

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Free Geometry Dash Cheats Gold Coins Stars Generator 2023-2024 ★★

Author(s):

Free Geometry Dash Cheats Gold Coins Stars Generator 2023-2024

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