Results 81 to 90 of about 9,543 (293)
Signed Projective Cubes, a Homomorphism Point of View
Journal of Graph Theory, EarlyView.ABSTRACT The (signed) projective cubes, as a special class of graphs closely related to the hypercubes, are on the crossroad of geometry, algebra, discrete mathematics and linear algebra. Defined as Cayley graphs on binary groups, they represent basic linear dependencies.
Meirun Chen +2 more
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Topological methods in zero-sum Ramsey theory
Forum of Mathematics, SigmaA landmark result of Erdős, Ginzburg, and Ziv (EGZ) states that any sequence of $2n-1$ elements in ${\mathbb {Z}}/n$ contains a zero-sum subsequence of length n.
Florian Frick +7 more
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Finite Euclidean Ramsey Theory
Journal of Combinatorial Theory, Series A, 1996 The author studies some problems of Euclidean Ramsey theory. He shows that in any two-coloring of the points of \(\mathbb{R}^4\) there will be four points forming a monochromatic unit square. He also improves the lower bounds for the chromatic numbers of the unit distance graphs of \(\mathbb{R}^4\) and \(\mathbb{R}^5\) to 7 and 9, respectively.
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On policy relevance of Ramsey tax rules [PDF]
, 2006 The Ramsey approach to optimal taxation and Ramsey tax rules have amassed substance in economic theory. However, they are often criticized on grounds of practicality, fairness, feasibility and some other aspects of designing actual tax policy. This paper
Selim, Sheikh Tareq, Cardiff University
core
On Tight Tree‐Complete Hypergraph Ramsey Numbers
Journal of Graph Theory, EarlyView.ABSTRACT Chvátal showed that for any tree T $T$ with k $k$ edges, the Ramsey number R ( T , n ) = k ( n − 1 ) + 1 $R(T,n)=k(n-1)+1$. For r = 3 $r=3$ or 4, we show that, if T $T$ is an r $r$‐uniform nontrivial tight tree, then the hypergraph Ramsey number R ( T , n ) = Θ ( n r − 1 ) $R(T,n)={\rm{\Theta }}({n}^{r-1})$.
Jiaxi Nie
wiley +1 more source
Ramsey theory for product spaces
, 2016 Ramsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics.
Vassilis Kanellopoulos +3 more
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On a Clique‐Building Game of Erdős
Journal of Graph Theory, EarlyView.ABSTRACT The following game was introduced in a list of open problems from 1983 attributed to Erdős: two players take turns claiming edges of a Kn ${K}_{n}$ until all edges are exhausted. Player 1 wins the game if the largest clique that they claim at the end is strictly larger than the largest clique of their opponent; otherwise, Player 2 wins the ...
Alexandru Malekshahian, Sam Spiro
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A linear upper bound in zero-sum Ramsey theory
International Journal of Mathematics and Mathematical Sciences, 1994 Let n, r and k be positive integers such that k|(nr). There exists a constant c(k,r) such that for fixed k and r and for every group A of order kR(Knr,A)≤n+c(k,r),where R(Knr,A) is the zero-sum Ramsey number introduced by Bialostocki and Dierker [1], and
Yair Caro
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CoRRIn 1955, Greenwood and Gleason showed that the Ramsey number R(3, 3, 3) = 17 by constructing an edge-chromatic graph on 16 vertices in three colors with no triangles. Their technique employed finite fields. This same result was obtained later by using another technique.
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, 2018 This thesis presents various types of results from Ramsey Theory, most particularly, Ramsey-type theorems concerning graphs and families of sets. This thesis consists of 8 chapters.
Chng, Zhi Yee
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