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Decomposing an eulerian graph into cycles. ★★

Author(s): Hajós

Conjecture   Every simple eulerian graph on $ n $ vertices can be decomposed into at most $ \frac{1}{2}(n-1) $ cycles.

Keywords:

Cycle Double Covers Containing Predefined 2-Regular Subgraphs ★★★

Author(s): Arthur; Hoffmann-Ostenhof

Conjecture   Let $ G $ be a $ 2 $-connected cubic graph and let $ S $ be a $ 2 $-regular subgraph such that $ G-E(S) $ is connected. Then $ G $ has a cycle double cover which contains $ S $ (i.e all cycles of $ S $).

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A funcoid related to directed topological spaces ★★

Author(s): Porton

Conjecture   Let $ R $ be the complete funcoid corresponding to the usual topology on extended real line $ [-\infty,+\infty] = \mathbb{R}\cup\{-\infty,+\infty\} $. Let $ \geq $ be the order on this set. Then $ R\sqcap^{\mathsf{FCD}}\mathord{\geq} $ is a complete funcoid.
Proposition   It is easy to prove that $ \langle R\sqcap^{\mathsf{FCD}}\mathord{\geq}\rangle \{x\} $ is the infinitely small right neighborhood filter of point $ x\in[-\infty,+\infty] $.

If proved true, the conjecture then can be generalized to a wider class of posets.

Keywords:

Weighted colouring of hexagonal graphs. ★★

Author(s): McDiarmid; Reed

Conjecture   There is an absolute constant $ c $ such that for every hexagonal graph $ G $ and vertex weighting $ p:V(G)\rightarrow \mathbb{N} $, $$\chi(G,p) \leq \frac{9}{8}\omega(G,p) + c $$

Keywords:

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

3-accessibility of Fibonacci numbers ★★

Author(s): Landman; Robertson

Question   Is the set of Fibonacci numbers 3-accessible?

Keywords: Fibonacci numbers; monochromatic diffsequences

Sidorenko's Conjecture ★★★

Author(s): Sidorenko

Conjecture   For any bipartite graph $ H $ and graph $ G $, the number of homomorphisms from $ H $ to $ G $ is at least $ \left(\frac{2|E(G)|}{|V(G)|^2}\right)^{|E(H)|}|V(G)|^{|V(H)|} $.

Keywords: density problems; extremal combinatorics; homomorphism

Working My Singing Monsters Cheats Generator Online (No Survey) ★★

Author(s):

Working My Singing Monsters Cheats Generator Online (No Survey)

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Are there only finite Fermat Primes? ★★★

Author(s):

Conjecture   A Fermat prime is a Fermat number \[ F_n  = 2^{2^n }  + 1 \] that is prime. The only known Fermat primes are F_0 =3,F_1=5,F_2=17,F_3 =257 ,F_4=65537 It is unknown if other fermat primes exist.

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Almost all non-Hamiltonian 3-regular graphs are 1-connected ★★

Author(s): Haythorpe

Conjecture   Denote by $ NH(n) $ the number of non-Hamiltonian 3-regular graphs of size $ 2n $, and similarly denote by $ NHB(n) $ the number of non-Hamiltonian 3-regular 1-connected graphs of size $ 2n $.

Is it true that $ \lim\limits_{n \rightarrow \infty} \displaystyle\frac{NHB(n)}{NH(n)} = 1 $?

Keywords: Hamiltonian, Bridge, 3-regular, 1-connected

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

Author(s):

Dragon Ball Z Dokkan Battle Cheats Generator 2024 (LEGIT)

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Dragon Ball Legends Cheats Generator Ios and Android 2024 (Working Generator) ★★

Author(s):

Dragon Ball Legends Cheats Generator Ios and Android 2024 (Working Generator)

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Every 4-connected toroidal graph has a Hamilton cycle ★★

Author(s): Grunbaum; Nash-Williams

Conjecture   Every 4-connected toroidal graph has a Hamilton cycle.

Keywords:

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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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.

Keywords:

Finite Lattice Representation Problem ★★★★

Author(s):

Conjecture  

There exists a finite lattice which is not the congruence lattice of a finite algebra.

Keywords: congruence lattice; finite algebra

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

Author(s):

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

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Toon Blast Cheats Generator Android Ios 2024 Cheats Generator (re-designed) ★★

Author(s):

Toon Blast Cheats Generator Android Ios 2024 Cheats Generator (re-designed)

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

Author(s):

Gta 5 Cheats Generator No Human Verification (Ios Android)

Keywords:

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

Author(s):

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

Keywords:

Dragon City Cheats Generator 2023-2024 Edition (Verified) ★★

Author(s):

Dragon City Cheats Generator 2023-2024 Edition (Verified)

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What is the homotopy type of the group of diffeomorphisms of the 4-sphere? ★★★★

Author(s): Smale

Problem   $ Diff(S^4) $ has the homotopy-type of a product space $ Diff(S^4) \simeq \mathbb O_5 \times Diff(D^4) $ where $ Diff(D^4) $ is the group of diffeomorphisms of the 4-ball which restrict to the identity on the boundary. Determine some (any?) homotopy or homology groups of $ Diff(D^4) $.

Keywords: 4-sphere; diffeomorphisms

Jones' conjecture ★★

Author(s): Kloks; Lee; Liu

For a graph $ G $, let $ cp(G) $ denote the cardinality of a maximum cycle packing (collection of vertex disjoint cycles) and let $ cc(G) $ denote the cardinality of a minimum feedback vertex set (set of vertices $ X $ so that $ G-X $ is acyclic).

Conjecture   For every planar graph $ G $, $ cc(G)\leq 2cp(G) $.

Keywords: cycle packing; feedback vertex set; planar graph

Odd-cycle transversal in triangle-free graphs ★★

Author(s): Erdos; Faudree; Pach; Spencer

Conjecture   If $ G $ is a simple triangle-free graph, then there is a set of at most $ n^2/25 $ edges whose deletion destroys every odd cycle.

Keywords:

New.updated Kim Kardashian Hollywood Cash Stars Cheats 2024 Free No Verification "Free" ★★

Author(s):

New.updated Kim Kardashian Hollywood Cash Stars Cheats 2024 Free No Verification "Free"

Keywords:

Signing a graph to have small magnitude eigenvalues ★★

Author(s): Bilu; Linial

Conjecture   If $ A $ is the adjacency matrix of a $ d $-regular graph, then there is a symmetric signing of $ A $ (i.e. replace some $ +1 $ entries by $ -1 $) so that the resulting matrix has all eigenvalues of magnitude at most $ 2 \sqrt{d-1} $.

Keywords: eigenvalue; expander; Ramanujan graph; signed graph; signing

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

Growth of finitely presented groups ★★★

Author(s): Adyan

Problem   Does there exist a finitely presented group of intermediate growth?

Keywords: finitely presented; growth

Inverse Galois Problem ★★★★

Author(s): Hilbert

Conjecture   Every finite group is the Galois group of some finite algebraic extension of $ \mathbb Q $.

Keywords:

Half-integral flow polynomial values ★★

Author(s): Mohar

Let $ \Phi(G,x) $ be the flow polynomial of a graph $ G $. So for every positive integer $ k $, the value $ \Phi(G,k) $ equals the number of nowhere-zero $ k $-flows in $ G $.

Conjecture   $ \Phi(G,5.5) > 0 $ for every 2-edge-connected graph $ G $.

Keywords: nowhere-zero flow

Nowhere-zero flows ★★

Author(s):

Nowhere-zero flows

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Finite entailment of Positive Horn logic ★★

Author(s): Martin

Question   Positive Horn logic (pH) is the fragment of FO involving exactly $ \exists, \forall, \wedge, = $. Does the fragment $ pH \wedge \neg pH $ have the finite model property?

Keywords: entailment; finite satisfiability; horn logic

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

Author(s):

SimCity BuildIt Cheats Generator 2024 (No Human Verification)

Keywords:

Nonseparating planar continuum ★★

Author(s):

Conjecture   Does any path-connected, compact set in the plane which does not separate the plane have the fixed point property?

A set has the fixed point property if every continuous map from it into itself has a fixed point.

Keywords: fixed point

War Dragons Rubies Cheats 2024 (re-designed) ★★

Author(s):

War Dragons Rubies Cheats 2024 (re-designed)

Keywords:

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

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)

Keywords:

Switching reconstruction conjecture ★★

Author(s): Stanley

Conjecture   Every simple graph on five or more vertices is switching-reconstructible.

Keywords: reconstruction

Free Real Racing 3 Cheats Generator 2024 (updated Generator) ★★

Author(s):

Free Real Racing 3 Cheats Generator 2024 (updated Generator)

Keywords:

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

Author(s):

Gardenscapes Cheats Generator 2024 for Android iOS (updated Generator)

Keywords:

Raid Shadow Legends Cheats Generator Unlimited IOS And Android No Survey 2024 (free!!) ★★

Author(s):

Raid Shadow Legends Cheats Generator Unlimited IOS And Android No Survey 2024 (free!!)

Keywords:

The Crossing Number of the Hypercube ★★

Author(s): Erdos; Guy

The crossing number $ cr(G) $ of $ G $ is the minimum number of crossings in all drawings of $ G $ in the plane.

The $ d $-dimensional (hyper)cube $ Q_d $ is the graph whose vertices are all binary sequences of length $ d $, and two of the sequences are adjacent in $ Q_d $ if they differ in precisely one coordinate.

Conjecture   $ \displaystyle \lim  \frac{cr(Q_d)}{4^d} = \frac{5}{32} $

Keywords: crossing number; hypercube

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:

Jaeger's modular orientation conjecture ★★★

Author(s): Jaeger

Conjecture   Every $ 4k $-edge-connected graph can be oriented so that $ {\mathit indegree}(v) - {\mathit outdegree}(v) \cong 0 $ (mod $ 2k+1 $) for every vertex $ v $.

Keywords: nowhere-zero flow; orientation

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

Author(s):

V-Bucks Generator Unlimited Generator (No Human Verification)

Keywords:

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

Author(s):

Match Masters Free Coins Cheats 2024 (FREE!)

Keywords:

Funcoidal products inside an inward reloid ★★

Author(s): Porton

Conjecture   (solved) If $ a \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} b \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f $ then $ a \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} b \subseteq f $ for every funcoid $ f $ and atomic f.o. $ a $ and $ b $ on the source and destination of $ f $ correspondingly.

A stronger conjecture:

Conjecture   If $ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{RLD}}}} \mathcal{B} \subseteq \left( \mathsf{\ensuremath{\operatorname{RLD}}} \right)_{\ensuremath{\operatorname{in}}} f $ then $ \mathcal{A} \times^{\mathsf{\ensuremath{\operatorname{FCD}}}} \mathcal{B} \subseteq f $ for every funcoid $ f $ and $ \mathcal{A} \in \mathfrak{F} \left( \ensuremath{\operatorname{Src}}f \right) $, $ \mathcal{B} \in \mathfrak{F} \left( \ensuremath{\operatorname{Dst}}f \right) $.

Keywords: inward reloid

The Riemann Hypothesis ★★★★

Author(s): Riemann

The zeroes of the Riemann zeta function that are inside the Critical Strip (i.e. the vertical strip of the complex plane where the real part of the complex variable is in ]0;1[), are actually located on the Critical line ( the vertical line of the complex plane with real part equal to 1/2)

Keywords: Millenium Problems; zeta

The Double Cap Conjecture ★★

Author(s): Kalai

Conjecture   The largest measure of a Lebesgue measurable subset of the unit sphere of $ \mathbb{R}^n $ containing no pair of orthogonal vectors is attained by two open caps of geodesic radius $ \pi/4 $ around the north and south poles.

Keywords: combinatorial geometry; independent set; orthogonality; projective plane; sphere

Linial-Berge path partition duality ★★★

Author(s): Berge; Linial

Conjecture   The minimum $ k $-norm of a path partition on a directed graph $ D $ is no more than the maximal size of an induced $ k $-colorable subgraph.

Keywords: coloring; directed path; partition