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Edge list coloring conjecture ★★★

Author(s):

Conjecture   Let $ G $ be a loopless multigraph. Then the edge chromatic number of $ G $ equals the list edge chromatic number of $ G $.

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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

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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Circular colouring the orthogonality graph ★★

Author(s): DeVos; Ghebleh; Goddyn; Mohar; Naserasr

Let $ {\mathcal O} $ denote the graph with vertex set consisting of all lines through the origin in $ {\mathbb R}^3 $ and two vertices adjacent in $ {\mathcal O} $ if they are perpendicular.

Problem   Is $ \chi_c({\mathcal O}) = 4 $?

Keywords: circular coloring; geometric graph; orthogonality

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.

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Seagull problem ★★

Author(s):

Seagull problem

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

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Dragon City Cheats Generator 2023-2024 Edition (Verified)

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War Dragons Rubies Cheats 2024 (rejuvenated cheats) ★★

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War Dragons Rubies Cheats 2024 (rejuvenated cheats)

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Goldbach conjecture ★★★★

Author(s): Goldbach

Conjecture   Every even integer greater than 2 is the sum of two primes.

Keywords: additive basis; prime

r-regular graphs are not uniquely hamiltonian. ★★★

Author(s): Sheehan

Conjecture   If $ G $ is a finite $ r $-regular graph, where $ r > 2 $, then $ G $ is not uniquely hamiltonian.

Keywords: hamiltonian; regular; uniquely hamiltonian

Lindelöf hypothesis ★★

Author(s): Lindelöf

Conjecture   For any $ \epsilon>0 $ $$\zeta\left(\frac12 + it\right) \mbox{ is }\mathcal{O}(t^\epsilon).$$

Since $ \epsilon $ can be replaced by a smaller value, we can also write the conjecture as, for any positive $ \epsilon $, $$\zeta\left(\frac12 + it\right) \mbox{ is }o(t^\varepsilon).$$

Keywords: Riemann Hypothesis; zeta

War Thunder Golden Eagles Generator Working Cheats (refreshed version) ★★

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War Thunder Golden Eagles Generator Working Cheats (refreshed version)

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Boom Beach Unlimited Diamonds Cheats Generator 2024 (fresh strategy) ★★

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Boom Beach Unlimited Diamonds Cheats Generator 2024 (fresh strategy)

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5-local-tensions ★★

Author(s): DeVos

Conjecture   There exists a fixed constant $ c $ (probably $ c=4 $ suffices) so that every embedded (loopless) graph with edge-width $ \ge c $ has a 5-local-tension.

Keywords: coloring; surface; tension

Atomicity of the poset of multifuncoids ★★

Author(s): Porton

Conjecture   The poset of 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

General position subsets ★★

Author(s): Gowers

Question   What is the least integer $ f(n) $ such that every set of at least $ f(n) $ points in the plane contains $ n $ collinear points or a subset of $ n $ points in general position (no three collinear)?

Keywords: general position subset, no-three-in-line problem

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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Fishdom Cheats Generator Cheats Generator 2023-2024 (Free!!) ★★

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Fishdom Cheats Generator Cheats Generator 2023-2024 (Free!!)

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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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Guide ★★

Author(s):

Guide

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My Singing Monsters Cheats Generator 2024 (rejuvenated Generator) ★★

Author(s):

My Singing Monsters Cheats Generator 2024 (rejuvenated Generator)

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Obstacle number of planar graphs

Author(s): Alpert; Koch; Laison

Does there exist a planar graph with obstacle number greater than 1? Is there some $ k $ such that every planar graph has obstacle number at most $ k $?

Keywords: graph drawing; obstacle number; planar graph; visibility graph

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

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

Consecutive non-orientable embedding obstructions ★★★

Author(s):

Conjecture   Is there a graph $ G $ that is a minor-minimal obstruction for two non-orientable surfaces?

Keywords: minor; surface

Perfect cuboid ★★

Author(s):

Conjecture   Does a perfect cuboid exist?

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Laplacian Degrees of a Graph ★★

Author(s): Guo

Conjecture   If $ G $ is a connected graph on $ n $ vertices, then $ c_k(G) \ge d_k(G) $ for $ k = 1, 2, \dots, n-1 $.

Keywords: degree sequence; Laplacian matrix

Partitioning edge-connectivity ★★

Author(s): DeVos

Question   Let $ G $ be an $ (a+b+2) $-edge-connected graph. Does there exist a partition $ \{A,B\} $ of $ E(G) $ so that $ (V,A) $ is $ a $-edge-connected and $ (V,B) $ is $ b $-edge-connected?

Keywords: edge-coloring; edge-connectivity

Chromatic Number of Common Graphs ★★

Author(s): Hatami; Hladký; Kráľ; Norine; Razborov

Question   Do common graphs have bounded chromatic number?

Keywords: common graph

Family Island Cheats Generator Pro Apk (Android Ios) ★★

Author(s):

Family Island Cheats Generator Pro Apk (Android Ios)

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KPZ Universality Conjectures ★★

Author(s):

Conjecture  

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Working Generator World Of Tanks Blitz Gold Credits Cheats Android Ios 2024 (HOT) ★★

Author(s):

Working Generator World Of Tanks Blitz Gold Credits Cheats Android Ios 2024 (HOT)

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Bleach Brave Souls Cheats Generator No Human Verification (Without Surveys) ★★

Author(s):

Bleach Brave Souls Cheats Generator No Human Verification (Without Surveys)

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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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Complexity of square-root sum ★★

Author(s): Goemans

Question   What is the complexity of the following problem?

Given $ a_1,\dots,a_n; k $, determine whether or not $  \sum_i \sqrt{a_i} \leq k.  $

Keywords: semi-definite programming

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

Author(s):

War Dragons Rubies Cheats Generator 2024 (improved version)

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Monochromatic empty triangles ★★★

Author(s):

If $ X \subseteq {\mathbb R}^2 $ is a finite set of points which is 2-colored, an empty triangle is a set $ T \subseteq X $ with $ |T|=3 $ so that the convex hull of $ T $ is disjoint from $ X \setminus T $. We say that $ T $ is monochromatic if all points in $ T $ are the same color.

Conjecture   There exists a fixed constant $ c $ with the following property. If $ X \subseteq {\mathbb R}^2 $ is a set of $ n $ points in general position which is 2-colored, then it has $ \ge cn^2 $ monochromatic empty triangles.

Keywords: empty triangle; general position; ramsey theory

Frankl's union-closed sets conjecture ★★

Author(s): Frankl

Conjecture   Let $ F $ be a finite family of finite sets, not all empty, that is closed under taking unions. Then there exists $ x $ such that $ x $ is an element of at least half the members of $ F $.

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Every metamonovalued funcoid is monovalued ★★

Author(s): Porton

Conjecture   Every metamonovalued funcoid is monovalued.

The reverse is almost trivial: Every monovalued funcoid is metamonovalued.

Keywords: monovalued

Rainbow Six Siege Cheats Generator Android Ios No Survey 2024 (Current Version) ★★

Author(s):

Rainbow Six Siege Cheats Generator Android Ios No Survey 2024 (Current Version)

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Perfect 2-error-correcting codes over arbitrary finite alphabets. ★★

Author(s):

Conjecture   Does there exist a nontrivial perfect 2-error-correcting code over any finite alphabet, other than the ternary Golay code?

Keywords: 2-error-correcting; code; existence; perfect; perfect code

Free Super Meat Boy Forever Cheats No Human Verification No Survey (2024 Method) ★★

Author(s):

Free Super Meat Boy Forever Cheats No Human Verification No Survey (2024 Method)

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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

PTAS for feedback arc set in tournaments ★★

Author(s): Ailon; Alon

Question   Is there a polynomial time approximation scheme for the feedback arc set problem for the class of tournaments?

Keywords: feedback arc set; PTAS; tournament

Graham's conjecture on tree reconstruction ★★

Author(s): Graham

Problem   for every graph $ G $, we let $ L(G) $ denote the line graph of $ G $. Given that $ G $ is a tree, can we determine it from the integer sequence $ |V(G)|, |V(L(G))|, |V(L(L(G)))|, \ldots $?

Keywords: reconstruction; tree

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

The Bermond-Thomassen Conjecture ★★

Author(s): Bermond; Thomassen

Conjecture   For every positive integer $ k $, every digraph with minimum out-degree at least $ 2k-1 $ contains $ k $ disjoint cycles.

Keywords: cycles

Subdivision of a transitive tournament in digraphs with large outdegree. ★★

Author(s): Mader

Conjecture   For all $ k $ there is an integer $ f(k) $ such that every digraph of minimum outdegree at least $ f(k) $ contains a subdivision of a transitive tournament of order $ k $.

Keywords:

V-Bucks Generator Free 2024 in 5 minutes (New Generator V-Bucks) ★★

Author(s):

V-Bucks Generator Free 2024 in 5 minutes (New Generator V-Bucks)

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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