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Free Generator Matchington Mansion Working Stars Coins Cheats (Matchington Mansion Generator)

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Toon Blast Cheats Generator 2024 (rejuvenated Generator) ★★

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Toon Blast Cheats Generator 2024 (rejuvenated Generator)

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Oriented trees in n-chromatic digraphs ★★★

Author(s): Burr

Conjecture   Every digraph with chromatic number at least $ 2k-2 $ contains every oriented tree of order $ k $ as a subdigraph.

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Sidorenko's Conjecture ★★★

Author(s): Sidorenko

Conjecture   For any bipartite graph $ H $ and graph $ G $, the number of homomorphisms from $ H $ to $ G $ is at least $ \left(\frac{2|E(G)|}{|V(G)|^2}\right)^{|E(H)|}|V(G)|^{|V(H)|} $.

Keywords: density problems; extremal combinatorics; homomorphism

Double-critical graph conjecture ★★

Author(s): Erdos; Lovasz

A connected simple graph $ G $ is called double-critical, if removing any pair of adjacent vertexes lowers the chromatic number by two.

Conjecture   $ K_n $ is the only $ n $-chromatic double-critical graph

Keywords: coloring; complete graph

Fishing Clash Cheats Generator Free in 2024 (Premium For Free) ★★

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Fishing Clash Cheats Generator Free in 2024 (Premium For Free)

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Convex uniform 5-polytopes ★★

Author(s):

Problem   Enumerate all convex uniform 5-polytopes.

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

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Jurassic Park Builder Cheats Generator 2024 No Human Verification (Real)

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Unconditional derandomization of Arthur-Merlin games ★★★

Author(s): Shaltiel; Umans

Problem   Prove unconditionally that $ \mathcal{AM} $ $ \subseteq $ $ \Sigma_2 $.

Keywords: Arthur-Merlin; Hitting Sets; unconditional

eFootball 2023 Cheats Generator IOS Android No Verification 2024 (NEW STRATEGY) ★★

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eFootball 2023 Cheats Generator IOS Android No Verification 2024 (NEW STRATEGY)

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What is the smallest number of disjoint spanning trees made a graph Hamiltonian ★★

Author(s): Goldengorin

We are given a complete simple undirected weighted graph $ G_1=(V,E) $ and its first arbitrary shortest spanning tree $ T_1=(V,E_1) $. We define the next graph $ G_2=(V,E\setminus E_1) $ and find on $ G_2 $ the second arbitrary shortest spanning tree $ T_2=(V,E_2) $. We continue similarly by finding $ T_3=(V,E_3) $ on $ G_3=(V,E\setminus \cup_{i=1}^{2}E_i) $, etc. Let k be the smallest number of disjoint shortest spanning trees as defined above and let $ T^{k}=(V,\cup_{i=1}^{k}E_i) $ be the graph obtained as union of all $ k $ disjoint trees.

Question 1. What is the smallest number of disjoint spanning trees creates a graph $ T^{k} $ containing a Hamiltonian path.

Question 2. What is the smallest number of disjoint spanning trees creates a graph $ T^{k} $ containing a shortest Hamiltonian path?

Questions 3 and 4. Replace in questions 1 and 2 a shortest spanning tree by a 1-tree. What is the smallest number of disjoint 1-trees creates a Hamiltonian graph? What is the smallest number of disjoint 1-trees creates a graph containing a shortest Hamiltonian cycle?

Keywords: 1-trees; cycle; Hamitonian path; spanning trees

Partial List Coloring ★★★

Author(s): Iradmusa

Let $ G $ be a simple graph, and for every list assignment $ \mathcal{L} $ let $ \lambda_{\mathcal{L}} $ be the maximum number of vertices of $ G $ which are colorable with respect to $ \mathcal{L} $. Define $ \lambda_t = \min{ \lambda_{\mathcal{L}} } $, where the minimum is taken over all list assignments $ \mathcal{L} $ with $ |\mathcal{L}| = t $ for all $ v \in V(G) $.

Conjecture   [2] Let $ G $ be a graph with list chromatic number $ \chi_\ell $ and $ 1\leq r\leq s\leq \chi_\ell $. Then \[\frac{\lambda_r}{r}\geq\frac{\lambda_s}{s}.\]

Keywords: list assignment; list coloring

Three-chromatic (0,2)-graphs ★★

Author(s): Payan

Question   Are there any (0,2)-graphs with chromatic number exactly three?

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Codes Free Star Stable Star Coins Jorvik Coins Cheats 2024 No Human Veryfication!!! ★★

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Codes Free Star Stable Star Coins Jorvik Coins Cheats 2024 No Human Veryfication!!!

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New.updated Kim Kardashian Hollywood Cash Stars Cheats 2024 Free No Verification "Free"

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Bouchet's 6-flow conjecture ★★★

Author(s): Bouchet

Conjecture   Every bidirected graph with a nowhere-zero $ k $-flow for some $ k $, has a nowhere-zero $ 6 $-flow.

Keywords: bidirected graph; nowhere-zero flow

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House Of Fun Cheats Generator 2024 for Android iOS (updated Generator)

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

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MONOPOLY GO Cheats Generator IOS Android No Verification 2024 (fresh method) ★★

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MONOPOLY GO Cheats Generator IOS Android No Verification 2024 (fresh method)

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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

Monochromatic reachability in arc-colored digraphs ★★★

Author(s): Sands; Sauer; Woodrow

Conjecture   For every $ k $, there exists an integer $ f(k) $ such that if $ D $ is a digraph whose arcs are colored with $ k $ colors, then $ D $ has a $ S $ set which is the union of $ f(k) $ stables sets so that every vertex has a monochromatic path to some vertex in $ S $.

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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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Melnikov's valency-variety problem

Author(s): Melnikov

Problem   The valency-variety $ w(G) $ of a graph $ G $ is the number of different degrees in $ G $. Is the chromatic number of any graph $ G $ with at least two vertices greater than $$\ceil{ \frac{\floor{w(G)/2}}{|V(G)| - w(G)} } ~ ?$$

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Hamiltonian cycles in powers of infinite graphs ★★

Author(s): Georgakopoulos

Conjecture  
    \item If $ G $ is a countable connected graph then its third power is hamiltonian. \item If $ G $ is a 2-connected countable graph then its square is hamiltonian.

Keywords: hamiltonian; infinite graph

¿Are critical k-forests tight? ★★

Author(s): Strausz

Conjecture  

Let $ H $ be a $ k $-uniform hypergraph. If $ H $ is a critical $ k $-forest, then it is a $ k $-tree.

Keywords: heterochromatic number

Pentagon problem ★★★

Author(s): Nesetril

Question   Let $ G $ be a 3-regular graph that contains no cycle of length shorter than $ g $. Is it true that for large enough~$ g $ there is a homomorphism $ G \to C_5 $?

Keywords: cubic; homomorphism

Almost all non-Hamiltonian 3-regular graphs are 1-connected ★★

Author(s): Haythorpe

Conjecture   Denote by $ NH(n) $ the number of non-Hamiltonian 3-regular graphs of size $ 2n $, and similarly denote by $ NHB(n) $ the number of non-Hamiltonian 3-regular 1-connected graphs of size $ 2n $.

Is it true that $ \lim\limits_{n \rightarrow \infty} \displaystyle\frac{NHB(n)}{NH(n)} = 1 $?

Keywords: Hamiltonian, Bridge, 3-regular, 1-connected

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

Author(s):

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

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Real roots of the flow polynomial ★★

Author(s): Welsh

Conjecture   All real roots of nonzero flow polynomials are at most 4.

Keywords: flow polynomial; nowhere-zero flow

Free Gardenscapes Coins Stars Cheats Pro Apk Online (2024) ★★

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Free Gardenscapes Coins Stars Cheats Pro Apk Online (2024)

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

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Cheats Free* Warzone COD points Cheats 2024 No Human Verification

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Free Jurassic Park Builder Cheats Generator Pro Apk (2024) ★★

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Free Jurassic Park Builder Cheats Generator Pro Apk (2024)

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Hamilton cycle in small d-diregular graphs ★★

Author(s): Jackson

An directed graph is $ k $-diregular if every vertex has indegree and outdegree at least $ k $.

Conjecture   For $ d >2 $, every $ d $-diregular oriented graph on at most $ 4d+1 $ vertices has a Hamilton cycle.

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Asymptotic Distribution of Form of Polyhedra ★★

Author(s): Rüdinger

Problem   Consider the set of all topologically inequivalent polyhedra with $ k $ edges. Define a form parameter for a polyhedron as $ \beta:= v/(k+2) $ where $ v $ is the number of vertices. What is the distribution of $ \beta $ for $ k \to \infty $?

Keywords: polyhedral graphs, distribution

Coloring random subgraphs ★★

Author(s): Bukh

If $ G $ is a graph and $ p \in [0,1] $, we let $ G_p $ denote a subgraph of $ G $ where each edge of $ G $ appears in $ G_p $ with independently with probability $ p $.

Problem   Does there exist a constant $ c $ so that $ {\mathbb E}(\chi(G_{1/2})) > c \frac{\chi(G)}{\log \chi(G)} $?

Keywords: coloring; random graph

Counting 3-colorings of the hex lattice ★★

Author(s): Thomassen

Problem   Find $ \lim_{n \rightarrow \infty} (\chi( H_n , 3)) ^{ 1 / |V(H_n)| } $.

Keywords: coloring; Lieb's Ice Constant; tiling; torus

Free Gta 5 Cheats Generator Pro Apk (2024) ★★

Author(s):

Free Gta 5 Cheats Generator Pro Apk (2024)

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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

War Machines Coins Diamonds Cheats 2024 (iOS Android) ★★

Author(s):

Conjecture  

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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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Coloring the union of degenerate graphs ★★

Author(s): Tarsi

Conjecture   The union of a $ 1 $-degenerate graph (a forest) and a $ 2 $-degenerate graph is $ 5 $-colourable.

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Free DealDash Bids Cheats Bids Generator 2023-2024 ★★

Author(s):

Free DealDash Bids Cheats Bids Generator 2023-2024

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Burnside problem ★★★★

Author(s): Burnside

Conjecture   If a group has $ r $ generators and exponent $ n $, is it necessarily finite?

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

Author(s):

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

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

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

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Cooking Fever Cheats Generator Latest Version 2024 For Free (WORKING Generator) ★★

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Cooking Fever Cheats Generator Latest Version 2024 For Free (WORKING Generator)

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Strong colorability ★★★

Author(s): Aharoni; Alon; Haxell

Let $ r $ be a positive integer. We say that a graph $ G $ is strongly $ r $-colorable if for every partition of the vertices to sets of size at most $ r $ there is a proper $ r $-coloring of $ G $ in which the vertices in each set of the partition have distinct colors.

Conjecture   If $ \Delta $ is the maximal degree of a graph $ G $, then $ G $ is strongly $ 2 \Delta $-colorable.

Keywords: strong coloring

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

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

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