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Ding's tau_r vs. tau conjecture ★★★

Author(s): Ding

Conjecture   Let $ r \ge 2 $ be an integer and let $ H $ be a minor minimal clutter with $ \frac{1}{r}\tau_r(H) < \tau(H) $. Then either $ H $ has a $ J_k $ minor for some $ k \ge 2 $ or $ H $ has Lehman's property.

Keywords: clutter; covering; MFMC property; packing

The permanent conjecture ★★

Author(s): Kahn

Conjecture   If $ A $ is an invertible $ n \times n $ matrix, then there is an $ n \times n $ submatrix $ B $ of $ [A A] $ so that $ perm(B) $ is nonzero.

Keywords: invertible; matrix; permanent

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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The sum of the two largest eigenvalues (Solved) ★★

Author(s):

The sum of the two largest eigenvalues (Solved)

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Every prism over a 3-connected planar graph is hamiltonian. ★★

Author(s): Kaiser; Král; Rosenfeld; Ryjácek; Voss

Conjecture   If $ G $ is a $ 3 $-connected planar graph, then $ G\square K_2 $ has a Hamilton cycle.

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Fasted Way! For Free Royal Match Coins Cheats Working 2024 Android Ios ★★

Author(s):

Fasted Way! For Free Royal Match Coins Cheats Working 2024 Android Ios

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Antidirected trees in digraphs ★★

Author(s): Addario-Berry; Havet; Linhares Sales; Reed; Thomassé

An antidirected tree is an orientation of a tree in which every vertex has either indegree 0 or outdergree 0.

Conjecture   Let $ D $ be a digraph. If $ |A(D)| > (k-2) |V(D)| $, then $ D $ contains every antidirected tree of order $ k $.

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Approximation ratio for k-outerplanar graphs ★★

Author(s): Bentz

Conjecture   Is the approximation ratio for the Maximum Edge Disjoint Paths (MaxEDP) or the Maximum Integer Multiflow problem (MaxIMF) bounded by a constant in $ k $-outerplanar graphs or tree-width graphs?

Keywords: approximation algorithms; planar graph; polynomial algorithm

8 Ball Pool Cash Free Cheats 2024 (generator!) ★★

Author(s):

8 Ball Pool Cash Free Cheats 2024 (generator!)

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"Working Cheats" Sims FreePlay Simoleons Life Points and Social Points Generator No Human Verification 2024 ★★

Author(s):

"Working Cheats" Sims FreePlay Simoleons Life Points and Social Points Generator No Human Verification 2024

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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

Easy! Unlimited Candy Crush Saga Golds Lives Go New Cheats Codes ★★

Author(s):

Easy! Unlimited Candy Crush Saga Golds Lives Go New Cheats Codes

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Yu Gi Oh Duel Links Cheats Generator 2024 (safe and working) ★★

Author(s):

Yu Gi Oh Duel Links Cheats Generator 2024 (safe and working)

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Hello ★★

Author(s):

Hello

http://www.openproblemgarden.org/op/hello

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Mapping planar graphs to odd cycles ★★★

Author(s): Jaeger

Conjecture   Every planar graph of girth $ \ge 4k $ has a homomorphism to $ C_{2k+1} $.

Keywords: girth; homomorphism; planar graph

Hungry Shark World Cheats Generator 2024 (fresh strategy) ★★

Author(s):

Hungry Shark World Cheats Generator 2024 (fresh strategy)

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The Ultimate Guide to Gardenscapes Cheats and Hacks: Boost Your Game in 2024 ★★

Author(s):

Conjecture  

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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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Bingo Blitz Cheats Generator Unlimited No Jailbreak (Premium) ★★

Author(s):

Bingo Blitz Cheats Generator Unlimited No Jailbreak (Premium)

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Are almost all graphs determined by their spectrum? ★★★

Author(s):

Problem   Are almost all graphs uniquely determined by the spectrum of their adjacency matrix?

Keywords: cospectral; graph invariant; spectrum

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"

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New-mathod! Free Bloons TD Battles Energy Medal Money Cheats 2024 (No Human Verification) ★★

Author(s):

New-mathod! Free Bloons TD Battles Energy Medal Money Cheats 2024 (No Human Verification)

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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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Easy! Unlimited Rise Of Kingdoms Cheats Generator codes (GLITCH) ★★

Author(s):

Easy! Unlimited Rise Of Kingdoms Cheats Generator codes (GLITCH)

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Saturated $k$-Sperner Systems of Minimum Size ★★

Author(s): Morrison; Noel; Scott

Question   Does there exist a constant $ c>1/2 $ and a function $ n_0(k) $ such that if $ |X|\geq n_0(k) $, then every saturated $ k $-Sperner system $ \mathcal{F}\subseteq \mathcal{P}(X) $ has cardinality at least $ 2^{(1+o(1))ck} $?

Keywords: antichain; extremal combinatorics; minimum saturation; saturation; Sperner system

FarmVille 2 Coins Farm Bucks Cheats in a few minutes new 2024 (No Survey) ★★

Author(s):

FarmVille 2 Coins Farm Bucks Cheats in a few minutes new 2024 (No Survey)

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Odd perfect numbers ★★★

Author(s): Ancient/folklore

Conjecture   There is no odd perfect number.

Keywords: perfect number

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

The stubborn list partition problem ★★

Author(s): Cameron; Eschen; Hoang; Sritharan

Problem   Does there exist a polynomial time algorithm which takes as input a graph $ G $ and for every vertex $ v \in V(G) $ a subset $ \ell(v) $ of $ \{1,2,3,4\} $, and decides if there exists a partition of $ V(G) $ into $ \{A_1,A_2,A_3,A_4\} $ so that $ v \in A_i $ only if $ i \in \ell(v) $ and so that $ A_1,A_2 $ are independent, $ A_4 $ is a clique, and there are no edges between $ A_1 $ and $ A_3 $?

Keywords: list partition; polynomial algorithm

Convex 'Fair' Partitions Of Convex Polygons ★★

Author(s): Nandakumar; Ramana

Basic Question: Given any positive integer n, can any convex polygon be partitioned into n convex pieces so that all pieces have the same area and same perimeter?

Definitions: Define a Fair Partition of a polygon as a partition of it into a finite number of pieces so that every piece has both the same area and the same perimeter. Further, if all the resulting pieces are convex, call it a Convex Fair Partition.

Questions: 1. (Rephrasing the above 'basic' question) Given any positive integer n, can any convex polygon be convex fair partitioned into n pieces?

2. If the answer to the above is "Not always'', how does one decide the possibility of such a partition for a given convex polygon and a given n? And if fair convex partition is allowed by a specific convex polygon for a give n, how does one find the optimal convex fair partition that minimizes the total length of the cut segments?

3. Finally, what could one say about higher dimensional analogs of this question?

Conjecture: The authors tend to believe that the answer to the above 'basic' question is "yes". In other words they guess: Every convex polygon allows a convex fair partition into n pieces for any n

Keywords: Convex Polygons; Partitioning

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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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.

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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

Coloring and immersion ★★★

Author(s): Abu-Khzam; Langston

Conjecture   For every positive integer $ t $, every (loopless) graph $ G $ with $ \chi(G) \ge t $ immerses $ K_t $.

Keywords: coloring; complete graph; immersion

5-flow conjecture ★★★★

Author(s): Tutte

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

Keywords: cubic; nowhere-zero flow

PK XD Generator Cheats 2024 Generator Cheats Tested On Android Ios (WORKING TIPS) ★★

Author(s):

PK XD Generator Cheats 2024 Generator Cheats Tested On Android Ios (WORKING TIPS)

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Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator (New 2024) ★★

Author(s):

Simpsons Tapped Out Cheats Generator Unlimited Cheats Generator (New 2024)

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Barnette's Conjecture ★★★

Author(s): Barnette

Conjecture   Every 3-connected cubic planar bipartite graph is Hamiltonian.

Keywords: bipartite; cubic; hamiltonian

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

Author(s):

eFootball 2023 Cheats Generator 2024 (WORKING IN 5 SECOND)

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Rank vs. Genus ★★★

Author(s): Johnson

Question   Is there a hyperbolic 3-manifold whose fundamental group rank is strictly less than its Heegaard genus? How much can the two differ by?

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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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Critical Ops Unlimited Credits Cheats IOS Android No Survey 2024 (FREE METHOD) ★★

Author(s):

Critical Ops Unlimited Credits Cheats IOS Android No Survey 2024 (FREE METHOD)

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Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!) ★★

Author(s):

Hungry Shark Evolution Cheats Generator IOS Android No Survey 2024 (Generator!)

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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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Legal Bleach Brave Souls Cheats Generator No Human Verification 2024 (No Surveys Needed) ★★

Author(s):

Legal Bleach Brave Souls Cheats Generator No Human Verification 2024 (No Surveys Needed)

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Warframe Free Platinum Cheats Free Generator 2024 in 5 minutes (successive cheats) ★★

Author(s):

Warframe Free Platinum Cheats Free Generator 2024 in 5 minutes (successive cheats)

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My Singing Monsters Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra) ★★

Author(s):

My Singing Monsters Cheats Generator 2024 Cheats Generator Tested On Android Ios (extra)

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Boom Beach Diamonds Generator Working Cheats (refreshed version) ★★

Author(s):

Boom Beach Diamonds Generator Working Cheats (refreshed version)

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P vs. BPP ★★★

Author(s): Folklore

Conjecture   Can all problems that can be computed by a probabilistic Turing machine (with error probability < 1/3) in polynomial time be solved by a deterministic Turing machine in polynomial time? That is, does P = BPP?

Keywords: BPP; circuit complexity; pseudorandom generators

Discrete Logarithm Problem ★★★

Author(s):

If $ p $ is prime and $ g,h \in {\mathbb Z}_p^* $, we write $ \log_g(h) = n $ if $ n \in {\mathbb Z} $ satisfies $ g^n =  h $. The problem of finding such an integer $ n $ for a given $ g,h \in {\mathbb Z}^*_p $ (with $ g \neq 1 $) is the Discrete Log Problem.

Conjecture   There does not exist a polynomial time algorithm to solve the Discrete Log Problem.

Keywords: discrete log; NP