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Dragon Ball Z Dokkan Battle Cheats Generator 2024 (FREE!) ★★

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Dragon Ball Z Dokkan Battle Cheats Generator 2024 (FREE!)

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Matchington Mansion Stars Coins Cheats IOS And Android No Verification Generator 2024 (fresh method) ★★

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Matchington Mansion Stars Coins Cheats IOS And Android No Verification Generator 2024 (fresh method)

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The Sims Mobile Cheats Generator Free 2024 No Verification Android iOS (tips codes) ★★

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The Sims Mobile Cheats Generator Free 2024 No Verification Android iOS (tips codes)

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Triangle free strongly regular graphs ★★★

Author(s):

Problem   Is there an eighth triangle free strongly regular graph?

Keywords: strongly regular; triangle free

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

Random stable roommates ★★

Author(s): Mertens

Conjecture   The probability that a random instance of the stable roommates problem on $ n \in 2{\mathbb N} $ people admits a solution is $ \Theta( n ^{-1/4} ) $.

Keywords: stable marriage; stable roommates

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

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

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Free Real Racing 3 Cheats Generator 2024 (updated Generator)

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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

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

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Brawlhalla Cheats Generator 2024 No Human Veryfication (codes)

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Switching reconstruction of digraphs ★★

Author(s): Bondy; Mercier

Question   Are there any switching-nonreconstructible digraphs on twelve or more vertices?

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Directed path of length twice the minimum outdegree ★★★

Author(s): Thomassé

Conjecture   Every oriented graph with minimum outdegree $ k $ contains a directed path of length $ 2k $.

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

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

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Imbalance conjecture ★★

Author(s): Kozerenko

Conjecture   Suppose that for all edges $ e\in E(G) $ we have $ imb(e)>0 $. Then $ M_{G} $ is graphic.

Keywords: edge imbalance; graphic sequences

Subgraph of large average degree and large girth. ★★

Author(s): Thomassen

Conjecture   For all positive integers $ g $ and $ k $, there exists an integer $ d $ such that every graph of average degree at least $ d $ contains a subgraph of average degree at least $ k $ and girth greater than $ g $.

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Edge-disjoint Hamilton cycles in highly strongly connected tournaments. ★★

Author(s): Thomassen

Conjecture   For every $ k\geq 2 $, there is an integer $ f(k) $ so that every strongly $ f(k) $-connected tournament has $ k $ edge-disjoint Hamilton cycles.

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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

Unused Free Bloons TD Battles Cheats No Human Verification No Survey (2024 Method) ★★

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Unused Free Bloons TD Battles Cheats No Human Verification No Survey (2024 Method)

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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

REAL* Free!! Bloons TD Battles Energy Medal Money Cheats Trick 2024 ★★

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REAL* Free!! Bloons TD Battles Energy Medal Money Cheats Trick 2024

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Mastering Subway Surfers: Your Ultimate Guide to Cheats, Hacks, and Generators ★★

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Conjecture  

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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

Does the chromatic symmetric function distinguish between trees? ★★

Author(s): Stanley

Problem   Do there exist non-isomorphic trees which have the same chromatic symmetric function?

Keywords: chromatic polynomial; symmetric function; tree

Free Clash of Clans Gems Cheats 2024 Edition Update (WORKS!) ★★

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Free Clash of Clans Gems Cheats 2024 Edition Update (WORKS!)

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

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

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Fishing Clash Cheats Generator IOS Android No Verification 2024 (Tips Strategy) ★★

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Fishing Clash Cheats Generator IOS Android No Verification 2024 (Tips Strategy)

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Domination in cubic graphs ★★

Author(s): Reed

Problem   Does every 3-connected cubic graph $ G $ satisfy $ \gamma(G) \le \lceil |G|/3 \rceil $ ?

Keywords: cubic graph; domination

Crossing sequences ★★

Author(s): Archdeacon; Bonnington; Siran

Conjecture   Let $ (a_0,a_1,a_2,\ldots,0) $ be a sequence of nonnegative integers which strictly decreases until $ 0 $.

Then there exists a graph that be drawn on a surface with orientable (nonorientable, resp.) genus $ i $ with $ a_i $ crossings, but not with less crossings.

Keywords: crossing number; crossing sequence

Chromatic number of associahedron ★★

Author(s): Fabila-Monroy; Flores-Penaloza; Huemer; Hurtado; Urrutia; Wood

Conjecture   Associahedra have unbounded chromatic number.

Keywords: associahedron, graph colouring, chromatic number

Big Line or Big Clique in Planar Point Sets ★★

Author(s): Kara; Por; Wood

Let $ S $ be a set of points in the plane. Two points $ v $ and $ w $ in $ S $ are visible with respect to $ S $ if the line segment between $ v $ and $ w $ contains no other point in $ S $.

Conjecture   For all integers $ k,\ell\geq2 $ there is an integer $ n $ such that every set of at least $ n $ points in the plane contains at least $ \ell $ collinear points or $ k $ pairwise visible points.

Keywords: Discrete Geometry; Geometric Ramsey Theory

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

Real Racing 3 Cheats Generator in a few minutes new Cheats Generator 2024 (No Survey) ★★

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Real Racing 3 Cheats Generator in a few minutes new Cheats Generator 2024 (No Survey)

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Unfriendly partitions ★★★

Author(s): Cowan; Emerson

If $ G $ is a graph, we say that a partition of $ V(G) $ is unfriendly if every vertex has at least as many neighbors in the other classes as in its own.

Problem   Does every countably infinite graph have an unfriendly partition into two sets?

Keywords: coloring; infinite graph; partition

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

Upgrading a completary multifuncoid ★★

Author(s): Porton

Let $ \mho $ be a set, $ \mathfrak{F} $ be the set of filters on $ \mho $ ordered reverse to set-theoretic inclusion, $ \mathfrak{P} $ be the set of principal filters on $ \mho $, let $ n $ be an index set. Consider the filtrator $ \left( \mathfrak{F}^n ; \mathfrak{P}^n \right) $.

Conjecture   If $ f $ is a completary multifuncoid of the form $ \mathfrak{P}^n $, then $ E^{\ast} f $ is a completary multifuncoid of the form $ \mathfrak{F}^n $.

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.

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Ramsey properties of Cayley graphs ★★★

Author(s): Alon

Conjecture   There exists a fixed constant $ c $ so that every abelian group $ G $ has a subset $ S \subseteq G $ with $ -S = S $ so that the Cayley graph $ {\mathit Cayley}(G,S) $ has no clique or independent set of size $ > c \log |G| $.

Keywords: Cayley graph; Ramsey number

Edge-antipodal colorings of cubes ★★

Author(s): Norine

We let $ Q_d $ denote the $ d $-dimensional cube graph. A map $ \phi : E(Q_d) \rightarrow \{0,1\} $ is called edge-antipodal if $ \phi(e) \neq \phi(e') $ whenever $ e,e' $ are antipodal edges.

Conjecture   If $ d \ge 2 $ and $ \phi : E(Q_d) \rightarrow \{0,1\} $ is edge-antipodal, then there exist a pair of antipodal vertices $ v,v' \in V(Q_d) $ which are joined by a monochromatic path.

Keywords: antipodal; cube; edge-coloring

The Crossing Number of the Complete Graph ★★★

Author(s):

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_n) =   \frac 14 \floor{\frac n2} \floor{\frac{n-1}2} \floor{\frac{n-2}2} \floor{\frac{n-3}2} $

Keywords: complete graph; crossing number

Inequality for square summable complex series ★★

Author(s): Retkes

Conjecture   For all $ \alpha=(\alpha_1,\alpha_2,\ldots)\in l_2(\cal{C}) $ the following inequality holds $$\sum_{n\geq 1}|\alpha_n|^2\geq \frac{6}{\pi^2}\sum_{k\geq0}\bigg| \sum_{l\geq0}\frac{1}{l+1}\alpha_{2^k(2l+1)}\bigg|^2 $$

Keywords: Inequality

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

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My Singing Monsters Cheats Generator 2024 (rejuvenated Generator)

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New World Of Tanks Blitz Free Gold Credits Cheats 2024 Tested (extra) ★★

Author(s):

New World Of Tanks Blitz Free Gold Credits Cheats 2024 Tested (extra)

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Diagonal Ramsey numbers ★★★★

Author(s): Erdos

Let $ R(k,k) $ denote the $ k^{th} $ diagonal Ramsey number.

Conjecture   $ \lim_{k \rightarrow \infty} R(k,k) ^{\frac{1}{k}} $ exists.
Problem   Determine the limit in the above conjecture (assuming it exists).

Keywords: Ramsey number

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

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

Genshin Impact Cheats Generator 2024 Edition Update (WORKS) ★★

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Genshin Impact Cheats Generator 2024 Edition Update (WORKS)

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Jurassic Park Builder Cheats Generator 2024 No Human Verification (Brand New) ★★

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Jurassic Park Builder Cheats Generator 2024 No Human Verification (Brand New)

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Fishing Clash Cheats Generator Free 2024 (New) ★★

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Fishing Clash Cheats Generator Free 2024 (New)

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P vs. NP ★★★★

Author(s): Cook; Levin

Problem   Is P = NP?

Keywords: Complexity Class; Computational Complexity; Millenium Problems; NP; P; polynomial algorithm

Free Warframe Platinum Cheats Pro Apk 2024 (Android Ios) ★★

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Free Warframe Platinum Cheats Pro Apk 2024 (Android Ios)

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Lords Mobile Cheats Unlimited Gems Coins Generator (No Human Verification) ★★

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Lords Mobile Cheats Unlimited Gems Coins Generator (No Human Verification)

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