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Circular flow numbers of $r$-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) $.

A $ (2t+1) $-regular graph $ G $ is a $ (2t+1) $-graph if $ |\partial_G(X)| \geq 2t+1 $ for every $ X \subseteq V(G) $ with $ |X| $ odd.

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

Keywords: flow conjectures; nowhere-zero flows

Lords Mobile Working Cheats Gems Coins Generator (NEW AND FREE) ★★

Author(s):

Lords Mobile Working Cheats Gems Coins Generator (NEW AND FREE)

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My Singing Monsters Cheats Generator Android Ios 2024 Cheats Generator (re-designed) ★★

Author(s):

My Singing Monsters Cheats Generator Android Ios 2024 Cheats Generator (re-designed)

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Grunbaum's Conjecture ★★★

Author(s): Grunbaum

Conjecture   If $ G $ is a simple loopless triangulation of an orientable surface, then the dual of $ G $ is 3-edge-colorable.

Keywords: coloring; surface

Turán Problem for $10$-Cycles in the Hypercube ★★

Author(s): Erdos

Problem   Bound the extremal number of $ C_{10} $ in the hypercube.

Keywords: cycles; extremal combinatorics; hypercube

Working Generator Boom Beach Diamonds Cheats Android Ios 2024 (HOT) ★★

Author(s):

Working Generator Boom Beach Diamonds Cheats Android Ios 2024 (HOT)

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

Author(s):

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

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Match Masters Free Coins Cheats 2024 (LEGIT) ★★

Author(s):

Match Masters Free Coins Cheats 2024 (LEGIT)

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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

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

Author(s):

SimCity BuildIt Cheats Generator No Human Verification (Without Surveys)

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Packing T-joins ★★

Author(s): DeVos

Conjecture   There exists a fixed constant $ c $ (probably $ c=1 $ suffices) so that every graft with minimum $ T $-cut size at least $ k $ contains a $ T $-join packing of size at least $ (2/3)k-c $.

Keywords: packing; T-join

Aharoni-Berger conjecture ★★★

Author(s): Aharoni; Berger

Conjecture   If $ M_1,\ldots,M_k $ are matroids on $ E $ and $ \sum_{i=1}^k rk_{M_i}(X_i) \ge \ell (k-1) $ for every partition $ \{X_1,\ldots,X_k\} $ of $ E $, then there exists $ X \subseteq E $ with $ |X| = \ell $ which is independent in every $ M_i $.

Keywords: independent set; matroid; partition

Hedetniemi's Conjecture ★★★

Author(s): Hedetniemi

Conjecture   If $ G,H $ are simple finite graphs, then $ \chi(G \times H) = \min \{ \chi(G), \chi(H) \} $.

Here $ G \times H $ is the tensor product (also called the direct or categorical product) of $ G $ and $ H $.

Keywords: categorical product; coloring; homomorphism; tensor product

Complexity of the H-factor problem. ★★

Author(s): Kühn; Osthus

An $ H $-factor in a graph $ G $ is a set of vertex-disjoint copies of $ H $ covering all vertices of $ G $.

Problem  Let $ c $ be a fixed positive real number and $ H $ a fixed graph. Is it NP-hard to determine whether a graph $ G $ on $ n $ vertices and minimum degree $ cn $ contains and $ H $-factor?

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Working Apex Legends Cheats Online Coins Generator (No Survey) ★★

Author(s):

Working Apex Legends Cheats Online Coins Generator (No Survey)

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

Author(s):

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

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Is Skewes' number e^e^e^79 an integer? ★★

Author(s):

Conjecture  

Skewes' number $ e^{e^{e^{79}}} $ is not an integer.

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The Two Color Conjecture ★★

Author(s): Neumann-Lara

Conjecture   If $ G $ is an orientation of a simple planar graph, then there is a partition of $ V(G) $ into $ \{X_1,X_2\} $ so that the graph induced by $ X_i $ is acyclic for $ i=1,2 $.

Keywords: acyclic; digraph; planar

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

Dirac's Conjecture ★★

Author(s): Dirac

Conjecture   For every set $ P $ of $ n $ points in the plane, not all collinear, there is a point in $ P $ contained in at least $ \frac{n}{2}-c $ lines determined by $ P $, for some constant $ c $.

Keywords: point set

The Borodin-Kostochka Conjecture ★★

Author(s): Borodin; Kostochka

Conjecture   Every graph with maximum degree $ \Delta \geq 9 $ has chromatic number at most $ \max\{\Delta-1, \omega\} $.

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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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Do any three longest paths in a connected graph have a vertex in common? ★★

Author(s): Gallai

Conjecture   Do any three longest paths in a connected graph have a vertex in common?

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Geometry Dash Free Gold Coins Stars Cheats 2024 (LEGIT) ★★

Author(s):

Geometry Dash Free Gold Coins Stars Cheats 2024 (LEGIT)

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Erdős–Straus conjecture ★★

Author(s): Erdos; Straus

Conjecture  

For all $ n > 2 $, there exist positive integers $ x $, $ y $, $ z $ such that $$1/x + 1/y + 1/z = 4/n$$.

Keywords: Egyptian fraction

Saturation in the Hypercube ★★

Author(s): Morrison; Noel; Scott

Question   What is the saturation number of cycles of length $ 2\ell $ in the $ d $-dimensional hypercube?

Keywords: cycles; hypercube; minimum saturation; saturation

Algebra ★★

Author(s):

Algebra

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

Author(s):

Dragon Ball Z Dokkan Battle Cheats Generator 2024 (LEGIT)

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Idle Miner Tycoon Cheats Generator 2023-2024 (No Human Verification) ★★

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Idle Miner Tycoon Cheats Generator 2023-2024 (No Human Verification)

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Rota's unimodal conjecture ★★★

Author(s): Rota

Let $ M $ be a matroid of rank $ r $, and for $ 0 \le i \le r $ let $ w_i $ be the number of closed sets of rank $ i $.

Conjecture   $ w_0,w_1,\ldots,w_r $ is unimodal.
Conjecture   $ w_0,w_1,\ldots,w_r $ is log-concave.

Keywords: flat; log-concave; matroid

Fishing Clash Cheats Generator 2024 No Verification Android iOS (new method) ★★

Author(s):

Fishing Clash Cheats Generator 2024 No Verification Android iOS (new method)

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eFootball 2023 Cheats Generator 2024 (WORKING IN 5 SECOND) ★★

Author(s):

eFootball 2023 Cheats Generator 2024 (WORKING IN 5 SECOND)

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Lucas Numbers Modulo m ★★

Author(s):

Conjecture   The sequence {L(n) mod m}, where L(n) are the Lucas numbers, contains a complete residue system modulo m if and only if m is one of the following: 2, 4, 6, 7, 14, 3^k, k >=1.

Keywords: Lucas numbers

REAL* Free!! Match Masters Coins Cheats Trick 2024 ★★

Author(s):

REAL* Free!! Match Masters Coins Cheats Trick 2024

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inverse of an integer matrix ★★

Author(s): Gregory

Question   I've been working on this for a long time and I'm getting nowhere. Could you help me or at least tell me where to look for help. Suppose D is an m-by-m diagonal matrix with integer elements all $ \ge 2 $. Suppose X is an m-by-n integer matrix $ (m \le n) $. Consider the partitioned matrix M = [D X]. Obviously M has full row rank so it has a right inverse of rational numbers. The question is, under what conditions does it have an integer right inverse? My guess, which I can't prove, is that the integers in each row need to be relatively prime.

Keywords: invertable matrices, integer matrices

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

Author(s):

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

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Fasted Way! For Free Star Stable Star Coins Jorvik Coins Cheats Working 2024 Android Ios ★★

Author(s):

Fasted Way! For Free Star Stable Star Coins Jorvik Coins Cheats Working 2024 Android Ios

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Nearly spanning regular subgraphs ★★★

Author(s): Alon; Mubayi

Conjecture   For every $ \epsilon > 0 $ and every positive integer $ k $, there exists $ r_0 = r_0(\epsilon,k) $ so that every simple $ r $-regular graph $ G $ with $ r \ge r_0 $ has a $ k $-regular subgraph $ H $ with $ |V(H)| \ge (1- \epsilon) |V(G)| $.

Keywords: regular; subgraph

Mixing Circular Colourings

Author(s): Brewster; Noel

Question   Is $ \mathfrak{M}_c(G) $ always rational?

Keywords: discrete homotopy; graph colourings; mixing

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

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Solution to the Lonely Runner Conjecture ★★

Author(s):

Solution to the Lonely Runner Conjecture

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War Thunder Unlimited Generator Golden Eagles Cheats IOS And Android No Survey 2024 (free!!) ★★

Author(s):

War Thunder Unlimited Generator Golden Eagles Cheats IOS And Android No Survey 2024 (free!!)

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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

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

Author(s):

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

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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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Forcing a $K_6$-minor ★★

Author(s): Barát ; Joret; Wood

Conjecture   Every graph with minimum degree at least 7 contains a $ K_6 $-minor.
Conjecture   Every 7-connected graph contains a $ K_6 $-minor.

Keywords: connectivity; graph minors

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

Monochromatic vertex colorings inherited from Perfect Matchings ★★★

Author(s):

Conjecture   For which values of $ n $ and $ d $ are there bi-colored graphs on $ n $ vertices and $ d $ different colors with the property that all the $ d $ monochromatic colorings have unit weight, and every other coloring cancels out?

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

Author(s):

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

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