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Circular flow number of regular class 1 graphs ★★

Author(s): Steffen

A nowhere-zero $ r $-flow $ (D(G),\phi) $ on $ G $ is an orientation $ D $ of $ G $ together with a function $ \phi $ from the edge set of $ G $ into the real numbers such that $ 1 \leq |\phi(e)| \leq r-1 $, for all $ e \in E(G) $, and $ \sum_{e \in E^+(v)}\phi(e) = \sum_{e \in E^-(v)}\phi(e), \textrm{ for all } v \in V(G) $. The circular flow number of $ G $ is inf$ \{ r | G $ has a nowhere-zero $ r $-flow $ \} $, and it is denoted by $ F_c(G) $.

A graph with maximum vertex degree $ k $ is a class 1 graph if its edge chromatic number is $ k $.

Conjecture   Let $ t \geq 1 $ be an integer and $ G $ a $ (2t+1) $-regular graph. If $ G $ is a class 1 graph, then $ F_c(G) \leq 2 + \frac{2}{t} $.

Keywords: nowhere-zero flow, edge-colorings, regular graphs

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Author(s):

Matchington Mansion Free Stars Coins Cheats Free Generator 2024 in 5 minutes (successive cheats)

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Cyclic spanning subdigraph with small cyclomatic number ★★

Author(s): Bondy

Conjecture   Let $ D $ be a digraph all of whose strong components are nontrivial. Then $ D $ contains a cyclic spanning subdigraph with cyclomatic number at most $ \alpha(D) $.

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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

Wide partition conjecture ★★

Author(s): Chow; Taylor

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

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Super Meat Boy Forever Points Cheats No Human Verification (Ios Android) ★★

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Super Meat Boy Forever Points Cheats No Human Verification (Ios Android)

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KPZ Universality Conjecture ★★★

Author(s):

Conjecture   Formulate a central limit theorem for the KPZ universality class.

Keywords: KPZ equation, central limit theorem

Dice Dreams Cheats Generator Get Free Dice Dreams Cheats Generator 2024 (Brand New) ★★

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Dice Dreams Cheats Generator Get Free Dice Dreams Cheats Generator 2024 (Brand New)

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Fixed-point logic with counting ★★

Author(s): Blass

Question   Can either of the following be expressed in fixed-point logic plus counting:
    \item Given a graph, does it have a perfect matching, i.e., a set $ M $ of edges such that every vertex is incident to exactly one edge from $ M $? \item Given a square matrix over a finite field (regarded as a structure in the natural way, as described in [BGS02]), what is its determinant?

Keywords: Capturing PTime; counting quantifiers; Fixed-point logic; FMT03-Bedlewo

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Conjecture  

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Geodesic cycles and Tutte's Theorem ★★

Author(s): Georgakopoulos; Sprüssel

Problem   If $ G $ is a $ 3 $-connected finite graph, is there an assignment of lengths $ \ell: E(G) \to \mathb R^+ $ to the edges of $ G $, such that every $ \ell $-geodesic cycle is peripheral?

Keywords: cycle space; geodesic cycles; peripheral cycles

Matching cut and girth ★★

Author(s):

Question   For every $ d $ does there exists a $ g $ such that every graph with average degree smaller than $ d $ and girth at least $ g $ has a matching-cut?

Keywords: matching cut, matching, cut

The 3n+1 conjecture ★★★

Author(s): Collatz

Conjecture   Let $ f(n) = 3n+1 $ if $ n $ is odd and $ \frac{n}{2} $ if $ n $ is even. Let $ f(1) = 1 $. Assume we start with some number $ n $ and repeatedly take the $ f $ of the current number. Prove that no matter what the initial number is we eventually reach $ 1 $.

Keywords: integer sequence

Special Primes

Author(s): George BALAN

Conjecture   Let $ p $ be a prime natural number. Find all primes $ q\equiv1\left(\mathrm{mod}\: p\right) $, such that $ 2^{\frac{\left(q-1\right)}{p}}\equiv1\left(\mathrm{mod}\: q\right) $.

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

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

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Match Masters Coins Cheats 2024 Update (FREE!!)

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Simultaneous partition of hypergraphs ★★

Author(s): Kühn; Osthus

Problem   Let $ H_1 $ and $ H_2 $ be two $ r $-uniform hypergraph on the same vertex set $ V $. Does there always exist a partition of $ V $ into $ r $ classes $ V_1, \dots , V_r $ such that for both $ i=1,2 $, at least $ r!m_i/r^r -o(m_i) $ hyperedges of $ H_i $ meet each of the classes $ V_1, \dots , V_r $?

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Author(s):

Candy Crush Saga Golds Lives Cheats 2024 Update Cheat (Verified)

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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

Magic square of squares ★★

Author(s): LaBar

Question   Does there exist a $ 3\times 3 $ magic square composed of distinct perfect squares?

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The 4x5 chessboard complex is the complement of a link, which link? ★★

Author(s): David Eppstein

Problem   Ian Agol and Matthias Goerner observed that the 4x5 chessboard complex is the complement of many distinct links in the 3-sphere. Their observation is non-constructive, as it uses the resolution of the Poincare Conjecture. Find specific links that have the 4x5 chessboard complex as their complement.

Keywords: knot theory, links, chessboard complex

Oriented chromatic number of planar graphs ★★

Author(s):

An oriented colouring of an oriented graph is assignment $ c $ of colours to the vertices such that no two arcs receive ordered pairs of colours $ (c_1,c_2) $ and $ (c_2,c_1) $. It is equivalent to a homomorphism of the digraph onto some tournament of order $ k $.

Problem   What is the maximal possible oriented chromatic number of an oriented planar graph?

Keywords: oriented coloring; oriented graph; planar graph

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

Author(s):

Conjecture  

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5-flow conjecture ★★★★

Author(s): Tutte

Conjecture   Every bridgeless graph has a nowhere-zero 5-flow.

Keywords: cubic; nowhere-zero flow

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

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Golf Battle Free Cheats Generator 999,999k Free 2024 (Free Generator)

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Lords Mobile Gems Coins Cheats Mod Android Ios No Survey 2024 (NEW) ★★

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Lords Mobile Gems Coins Cheats Mod Android Ios No Survey 2024 (NEW)

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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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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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Edge-Colouring Geometric Complete Graphs ★★

Author(s): Hurtado

Question   What is the minimum number of colours such that every complete geometric graph on $ n $ vertices has an edge colouring such that:
    \item[Variant A] crossing edges get distinct colours, \item[Variant B] disjoint edges get distinct colours, \item[Variant C] non-disjoint edges get distinct colours, \item[Variant D] non-crossing edges get distinct colours.

Keywords: geometric complete graph, colouring

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

Author(s):

Call Of Duty Mobile Cheats Generator 2024 (FREE!)

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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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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

4-regular 4-chromatic graphs of high girth ★★

Author(s): Grunbaum

Problem   Do there exist 4-regular 4-chromatic graphs of arbitrarily high girth?

Keywords: coloring; girth

Total Colouring Conjecture ★★★

Author(s): Behzad

Conjecture   A total coloring of a graph $ G = (V,E) $ is an assignment of colors to the vertices and the edges of $ G $ such that every pair of adjacent vertices, every pair of adjacent edges and every vertex and incident edge pair, receive different colors. The total chromatic number of a graph $ G $, $ \chi''(G) $, equals the minimum number of colors needed in a total coloring of $ G $. It is an old conjecture of Behzad that for every graph $ G $, the total chromatic number equals the maximum degree of a vertex in $ G $, $ \Delta(G) $ plus one or two. In other words, \[\chi''(G)=\Delta(G)+1\ \ or \ \ \Delta(G)+2.\]

Keywords: Total coloring

Triangle-packing vs triangle edge-transversal. ★★

Author(s): Tuza

Conjecture   If $ G $ has at most $ k $ edge-disjoint triangles, then there is a set of $ 2k $ edges whose deletion destroys every triangle.

Keywords:

A conjecture on iterated circumcentres ★★

Author(s): Goddyn

Conjecture   Let $ p_1,p_2,p_3,\ldots $ be a sequence of points in $ {\mathbb R}^d $ with the property that for every $ i \ge d+2 $, the points $ p_{i-1}, p_{i-2}, \ldots p_{i-d-1} $ are distinct, lie on a unique sphere, and further, $ p_i $ is the center of this sphere. If this sequence is periodic, must its period be $ 2d+4 $?

Keywords: periodic; plane geometry; sequence

Graphs with a forbidden induced tree are chi-bounded ★★★

Author(s): Gyarfas

Say that a family $ {\mathcal F} $ of graphs is $ \chi $-bounded if there exists a function $ f: {\mathbb N} \rightarrow {\mathbb N} $ so that every $ G \in {\mathcal F} $ satisfies $ \chi(G) \le f (\omega(G)) $.

Conjecture   For every fixed tree $ T $, the family of graphs with no induced subgraph isomorphic to $ T $ is $ \chi $-bounded.

Keywords: chi-bounded; coloring; excluded subgraph; tree

Critical Ops Cheats 2024 Working (Credits Generator) ★★

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Critical Ops Cheats 2024 Working (Credits Generator)

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FarmVille 2 Coins Farm Bucks Cheats Generator IOS Android No Verification 2024 (NEW STRATEGY) ★★

Author(s):

FarmVille 2 Coins Farm Bucks Cheats Generator IOS Android No Verification 2024 (NEW STRATEGY)

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Polignac's Conjecture ★★★

Author(s): de Polignac

Conjecture   Polignac's Conjecture: For any positive even number n, there are infinitely many prime gaps of size n. In other words: There are infinitely many cases of two consecutive prime numbers with difference n.

In particular, this implies:

Conjecture   Twin Prime Conjecture: There are an infinite number of twin primes.

Keywords: prime; prime gap

Free Generator Sims FreePlay Working Simoleons Life Points and Social Points Cheats (Sims FreePlay Generator) ★★

Author(s):

Free Generator Sims FreePlay Working Simoleons Life Points and Social Points Cheats (Sims FreePlay Generator)

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Antichains in the cycle continuous order ★★

Author(s): DeVos

If $ G $,$ H $ are graphs, a function $ f : E(G) \rightarrow E(H) $ is called cycle-continuous if the pre-image of every element of the (binary) cycle space of $ H $ is a member of the cycle space of $ G $.

Problem   Does there exist an infinite set of graphs $ \{G_1,G_2,\ldots \} $ so that there is no cycle continuous mapping between $ G_i $ and $ G_j $ whenever $ i \neq j $ ?

Keywords: antichain; cycle; poset

House Of Fun Cheats Generator Free Cheats Generator 2024 No Verification (Android iOS) ★★

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House Of Fun Cheats Generator Free Cheats Generator 2024 No Verification (Android iOS)

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Coin Master Spins Coins Cheats No Human Verification (Ios Android) ★★

Author(s):

Coin Master Spins Coins Cheats No Human Verification (Ios Android)

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Vertex Cover Integrality Gap ★★

Author(s): Atserias

Conjecture   For every $ \varepsilon > 0 $ there is $ \delta > 0 $ such that, for every large $ n $, there are $ n $-vertex graphs $ G $ and $ H $ such that $ G \equiv_{\delta n}^{\mathrm{C}} H $ and $ \mathrm{vc}(G) \ge (2 - \varepsilon) \cdot \mathrm{vc}(H) $.

Keywords: counting quantifiers; FMT12-LesHouches

Edge-Unfolding Convex Polyhedra ★★

Author(s): Shephard

Conjecture   Every convex polyhedron has a (nonoverlapping) edge unfolding.

Keywords: folding; nets

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

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

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Match Masters Free Coins Cheats 2024 (FREE!)

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Cheats Free* Warzone COD points Cheats 2024 No Human Verification ★★

Author(s):

Cheats Free* Warzone COD points Cheats 2024 No Human Verification

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