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339
Rainbows in the hypercube
, 2004
"... Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary ntuples and two vertices are adjacent iff the corresponding ntuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G, H) be the largest ..."
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Let Qn be a hypercube of dimension n, that is, a graph whose vertices are binary ntuples and two vertices are adjacent iff the corresponding ntuples differ in exactly one position. An edge coloring of a graph H is called rainbow if no two edges of H have the same color. Let f(G, H) be the largest
Rainbow copies of C4 in edgecolored hypercubes
, 2013
"... For positive integers k and d such that 4 ≤ k < d and k 6 = 5, we determine the maximum number of rainbow colored copies of C4 in a kedgecoloring of the ddimensional hypercube Qd. Interestingly, the kedgecolorings of Qd yielding the maximum number of rainbow copies of C4 also have the prop ..."
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For positive integers k and d such that 4 ≤ k < d and k 6 = 5, we determine the maximum number of rainbow colored copies of C4 in a kedgecoloring of the ddimensional hypercube Qd. Interestingly, the kedgecolorings of Qd yielding the maximum number of rainbow copies of C4 also have
Hypercube viewer
"... Efficient viewing and interacting with multidimensional data volumes is an essential part of many scientific fields. This interaction ranges from simple visualization to steering computationally demanding tasks. The mixing of computation and interpretation requires a library that allows user inputs ..."
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Efficient viewing and interacting with multidimensional data volumes is an essential part of many scientific fields. This interaction ranges from simple visualization to steering computationally demanding tasks. The mixing of computation and interpretation requires a library that allows user inputs and generated results to easily be transferred We wrote Hyperview in C++ using the QT library to facilitate this interaction. We describe the graphical user interface to the library and the basic design principles. We demonstrate the flexibility of the underlying libraries through a simple semblance picking application.
Turán’s theorem in the hypercube
 SIAM Journal on Discrete Mathematics
"... We are motivated by the analogue of Turán’s theorem in the hypercube Qn: how many edges can a Qdfree subgraph of Qn have? We study this question through its Ramseytype variant and obtain asymptotic results. We show that for every odd d it is possible to color the edges of Qn with (d+1)2 4 colors, ..."
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Cited by 12 (1 self)
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We are motivated by the analogue of Turán’s theorem in the hypercube Qn: how many edges can a Qdfree subgraph of Qn have? We study this question through its Ramseytype variant and obtain asymptotic results. We show that for every odd d it is possible to color the edges of Qn with (d+1)2 4 colors
Queue layouts of hypercubes
, 2011
"... A queue layout of a graph consists of a linear ordering σ of its vertices, and a partition of its edges into sets, called queues, such that in each set no two edges are nested with respect to σ. We show that the ndimensional hypercube Qn has a layout into n−⌊log2 n⌋ queues for all n ≥ 1. On the oth ..."
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A queue layout of a graph consists of a linear ordering σ of its vertices, and a partition of its edges into sets, called queues, such that in each set no two edges are nested with respect to σ. We show that the ndimensional hypercube Qn has a layout into n−⌊log2 n⌋ queues for all n ≥ 1
Coloring the cube with rainbow cycles
, 2012
"... For every even positive integer k ≥ 4 let f(n, k) denote the minimim number of colors required to color the edges of the ndimensional cube Qn, so that the edges of every copy of the kcycle Ck receive k distinct colors. Faudree, Gyárfás, Lesniak and Schelp proved that f(n, 4) = n for n = 4 or n> ..."
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Cited by 1 (0 self)
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For every even positive integer k ≥ 4 let f(n, k) denote the minimim number of colors required to color the edges of the ndimensional cube Qn, so that the edges of every copy of the kcycle Ck receive k distinct colors. Faudree, Gyárfás, Lesniak and Schelp proved that f(n, 4) = n for n = 4 or n> 5. We consider larger k and prove that if k ≡ 0 (mod 4), then there are positive constants c1, c2 depending only on k such that c1n k/4 < f(n, k) < c2n k/4. Our upper bound uses an old construction of Bose and Chowla of generalized Sidon sets. For k ≡ 2 (mod 4), the situation seems more complicated. For the smallest case k = 6 we show that n ≤ f(n, 6) < n 1+o(1). The upper bound is obtained from Behrend’s construction of a subset of the integers with no three term arithmetic progression.
Rainbow triangles in threecolored graphs
, 2014
"... Erdős and Sós proposed a problem of determining the maximum number F (n) of rainbow triangles in 3edgecolored complete graphs on n vertices. They conjectured that F (n) = F (a)+ F (b) +F (c) +F (d) + abc+ abd+ acd+ bcd, where a+ b+ c+ d = n and a, b, c, d are as equal as possible. We prove that ..."
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Erdős and Sós proposed a problem of determining the maximum number F (n) of rainbow triangles in 3edgecolored complete graphs on n vertices. They conjectured that F (n) = F (a)+ F (b) +F (c) +F (d) + abc+ abd+ acd+ bcd, where a+ b+ c+ d = n and a, b, c, d are as equal as possible. We prove
and
"... Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and nonexistence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above b ..."
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Rainbow connection number of Cartesian products and their subgraphs are considered. Previously known bounds are compared and nonexistence of such bounds for subgraphs of products are discussed. It is shown that the rainbow connection number of an isometric subgraph of a hypercube is bounded above
Results 1  10
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