Random

Dragon Ball Legends Cheats Generator (Ios Android) ★★

Author(s):

Dragon Ball Legends Cheats Generator (Ios Android)

Keywords:

Point sets with no empty pentagon

Author(s): Wood

Problem   Classify the point sets with no empty pentagon.

Keywords: combinatorial geometry; visibility graph

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

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

Author(s):

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

Keywords:

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

Author(s):

Brawlhalla Cheats Generator 2024 No Human Veryfication (codes)

Keywords:

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

Author(s):

Match Masters Free Coins Cheats 2024 (FREE!)

Keywords:

Apex Legends Coins Cheats 2024 (rejuvenated cheats) ★★

Author(s):

Apex Legends Coins Cheats 2024 (rejuvenated cheats)

Keywords:

Wide partition conjecture ★★

Author(s): Chow; Taylor

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

Keywords:

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

Edge Reconstruction Conjecture ★★★

Author(s): Harary

Conjecture  

Every simple graph with at least 4 edges is reconstructible from it's edge deleted subgraphs

Keywords: reconstruction

Number of Cliques in Minor-Closed Classes ★★

Author(s): Wood

Question   Is there a constant $ c $ such that every $ n $-vertex $ K_t $-minor-free graph has at most $ c^tn $ cliques?

Keywords: clique; graph; minor

Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!) ★★

Author(s):

Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!)

Keywords:

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

New Update: Sims FreePlay Free Simoleons Life Points and Social Points Cheats 2024 No Human Verification ★★

Author(s):

New Update: Sims FreePlay Free Simoleons Life Points and Social Points Cheats 2024 No Human Verification

Keywords:

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

Stable set meeting all longest directed paths. ★★

Author(s): Laborde; Payan; Xuong N.H.

Conjecture   Every digraph has a stable set meeting all longest directed paths

Keywords:

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

Author(s):

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

Keywords:

The Erdös-Hajnal Conjecture ★★★

Author(s): Erdos; Hajnal

Conjecture   For every fixed graph $ H $, there exists a constant $ \delta(H) $, so that every graph $ G $ without an induced subgraph isomorphic to $ H $ contains either a clique or an independent set of size $ |V(G)|^{\delta(H)} $.

Keywords: induced subgraph

Fishdom Cheats Generator without verification (Free) ★★

Author(s):

Fishdom Cheats Generator without verification (Free)

Keywords:

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

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

Algebra ★★

Author(s):

Algebra

Keywords:

Partitioning the Projective Plane ★★

Author(s): Noel

Throughout this post, by projective plane we mean the set of all lines through the origin in $ \mathbb{R}^3 $.

Definition   Say that a subset $ S $ of the projective plane is octahedral if all lines in $ S $ pass through the closure of two opposite faces of a regular octahedron centered at the origin.
Definition   Say that a subset $ S $ of the projective plane is weakly octahedral if every set $ S'\subseteq S $ such that $ |S'|=3 $ is octahedral.
Conjecture   Suppose that the projective plane can be partitioned into four sets, say $ S_1,S_2,S_3 $ and $ S_4 $ such that each set $ S_i $ is weakly octahedral. Then each $ S_i $ is octahedral.

Keywords: Partitioning; projective plane

V-Bucks Generator Unlimited Generator (No Human Verification) ★★

Author(s):

V-Bucks Generator Unlimited Generator (No Human Verification)

Keywords:

SimCity BuildIt Cheats Generator No Human Verification (Without Surveys) ★★

Author(s):

SimCity BuildIt Cheats Generator No Human Verification (Without Surveys)

Keywords:

Frobenius number of four or more integers ★★

Author(s):

Problem   Find an explicit formula for Frobenius number $ g(a_1, a_2, \dots, a_n) $ of co-prime positive integers $ a_1, a_2, \dots, a_n $ for $ n\geq 4 $.

Keywords:

F_d versus F_{d+1} ★★★

Author(s): Krajicek

Problem   Find a constant $ k $ such that for any $ d $ there is a sequence of tautologies of depth $ k $ that have polynomial (or quasi-polynomial) size proofs in depth $ d+1 $ Frege system $ F_{d+1} $ but requires exponential size $ F_d $ proofs.

Keywords: Frege system; short proof

Simpsons Tapped Out Donuts Cash Cheats 2024 (Ios Android) ★★

Author(s):

Simpsons Tapped Out Donuts Cash Cheats 2024 (Ios Android)

Keywords:

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)

Keywords:

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

FarmVille 2 Unlimited Coins Farm Bucks Cheats 2024 (WORKING IN 5 SECOND) ★★

Author(s):

FarmVille 2 Unlimited Coins Farm Bucks Cheats 2024 (WORKING IN 5 SECOND)

Keywords:

MONOPOLY GO Cheats Generator 2024 (fresh strategy) ★★

Author(s):

MONOPOLY GO Cheats Generator 2024 (fresh strategy)

Keywords:

Weak pentagon problem ★★

Author(s): Samal

Conjecture   If $ G $ is a cubic graph not containing a triangle, then it is possible to color the edges of $ G $ by five colors, so that the complement of every color class is a bipartite graph.

Keywords: Clebsch graph; cut-continuous mapping; edge-coloring; homomorphism; pentagon

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

Unused Free Kim Kardashian Hollywood Cheats No Human Verification No Survey (2024 Method) ★★

Author(s):

Unused Free Kim Kardashian Hollywood Cheats No Human Verification No Survey (2024 Method)

Keywords:

Decomposing eulerian graphs ★★★

Author(s):

Conjecture   If $ G $ is a 6-edge-connected Eulerian graph and $ P $ is a 2-transition system for $ G $, then $ (G,P) $ has a compaible decomposition.

Keywords: cover; cycle; Eulerian

My Singing Monsters Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra) ★★

Author(s):

My Singing Monsters Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra)

Keywords:

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

8 Ball Pool Free Cash Cheats Fully Works No Survey (Cheats) ★★

Author(s):

8 Ball Pool Free Cash Cheats Fully Works No Survey (Cheats)

Keywords:

"Working Cheats" Subway Surfers Coins Keys Generator Ios Android 2024 ★★

Author(s):

"Working Cheats" Subway Surfers Coins Keys Generator Ios Android 2024

Keywords:

Call Of Duty Mobile Cheats Generator 2024 (FREE!) ★★

Author(s):

Call Of Duty Mobile Cheats Generator 2024 (FREE!)

Keywords:

Rise Of Kingdoms Cheats Generator 2023-2024 Edition (Verified) ★★

Author(s):

Rise Of Kingdoms Cheats Generator 2023-2024 Edition (Verified)

Keywords:

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

Author(s):

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

Keywords:

Transversal achievement game on a square 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 a set of $ n $ cells having no two cells in the same row or column is the winner. What is the outcome of the game given optimal play?

Keywords: game

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

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.

Keywords:

Rainbow Six Siege Cheats Generator Latest Version 2024 New Cheats Generator (Unique) ★★

Author(s):

Rainbow Six Siege Cheats Generator Latest Version 2024 New Cheats Generator (Unique)

Keywords:

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

Subgroup formed by elements of order dividing n ★★

Author(s): Frobenius

Conjecture  

Suppose $ G $ is a finite group, and $ n $ is a positive integer dividing $ |G| $. Suppose that $ G $ has exactly $ n $ solutions to $ x^{n} = 1 $. Does it follow that these solutions form a subgroup of $ G $?

Keywords: order, dividing

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