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373
A HYPERCUBE PROBLEM
, 1988
"... The ndimensional hypercube, Qn, is the graph whose vertex set, V(Qn), is the set of all nbit strings, any two of which are adjacent iff they differ in exactly one bit. We refer to Qn as the ncube. The 1, 2, 3, and 4cubes ..."
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The ndimensional hypercube, Qn, is the graph whose vertex set, V(Qn), is the set of all nbit strings, any two of which are adjacent iff they differ in exactly one bit. We refer to Qn as the ncube. The 1, 2, 3, and 4cubes
Upper bounds on the size of 4 and 6cyclefree subgraphs of the hypercube
, 2011
"... In this paper we modify slightly Razborov’s flag algebra machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges of a 4cyclefree subgraph of the ndimensional hypercube is at most 0.6068 times the number of its edges. We also improve the upp ..."
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Cited by 11 (4 self)
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In this paper we modify slightly Razborov’s flag algebra machinery to be suitable for the hypercube. We use this modified method to show that the maximum number of edges of a 4cyclefree subgraph of the ndimensional hypercube is at most 0.6068 times the number of its edges. We also improve
New bounds on a hypercube coloring problem and linear codes
, 2000
"... In studying the scalability of optical networks, one problem arising involves coloring the vertices of the ndimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of O/_k(n), the minimu ..."
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Cited by 2 (0 self)
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In studying the scalability of optical networks, one problem arising involves coloring the vertices of the ndimensional hypercube with as few colors as possible such that any two vertices whose Hamming distance is at most k are colored differently. Determining the exact value of O/_k(n
Adjacent Vertices Faulttolerance Fanability of Hypercube
, 2006
"... In this paper, we introduce the concepts of fault tolerant fanability. We show that the ndimensional hypercube Qn are fadjacent and l edges fault tolerant (n − f − l) ∗fanable for n ≥ 3, f + l ≤ n − 2 and l ≥ 1. ..."
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In this paper, we introduce the concepts of fault tolerant fanability. We show that the ndimensional hypercube Qn are fadjacent and l edges fault tolerant (n − f − l) ∗fanable for n ≥ 3, f + l ≤ n − 2 and l ≥ 1.
Routing Permutations and 21 Routing Requests in the Hypercube
, 2000
"... Let H n be the directed symmetric ndimensional hypercube. Using the computer, we show that for any permutation of the vertices of H 4 , there exists a system of pairwise arcdisjoint directed paths from each vertex to its target in the permutation. This veries Szymanski's conjecture [8] for n ..."
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Cited by 2 (0 self)
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Let H n be the directed symmetric ndimensional hypercube. Using the computer, we show that for any permutation of the vertices of H 4 , there exists a system of pairwise arcdisjoint directed paths from each vertex to its target in the permutation. This veries Szymanski's conjecture [8] for n
On a Hypercube Coloring Problem
"... Let k (n) denote the minimum number of colors necessary to color the ndimensional hypercube so that no two vertices that are at distance at most k from each other get the same color. In other words, this is the smallest number of binary codes with minimum distance k + 1 that form a partition o ..."
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Cited by 10 (0 self)
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Let k (n) denote the minimum number of colors necessary to color the ndimensional hypercube so that no two vertices that are at distance at most k from each other get the same color. In other words, this is the smallest number of binary codes with minimum distance k + 1 that form a partition
OPTIMAL COADAPTED COUPLING FOR THE SYMMETRIC RANDOM WALK ON THE HYPERCUBE
, 2008
"... Let X and Y be two simple symmetric continuoustime random walks on the vertices of the ndimensional hypercube, Z n 2. We consider the class of coadapted couplings of these processes, and describe an intuitive coupling which is shown to be the fastest in this class. ..."
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Cited by 5 (3 self)
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Let X and Y be two simple symmetric continuoustime random walks on the vertices of the ndimensional hypercube, Z n 2. We consider the class of coadapted couplings of these processes, and describe an intuitive coupling which is shown to be the fastest in this class.
DimensionFree L2 Maximal Inequality for Spherical Means in the Hypercube
, 2014
"... We establish the maximal inequality claimed in the title. In combinatorial terms this has the implication that for sufficiently small ε> 0, for all n, any marking of an ε fraction of the vertices of the ndimensional hypercube necessarily leaves a vertex x such that marked vertices are a minorit ..."
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Cited by 1 (1 self)
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We establish the maximal inequality claimed in the title. In combinatorial terms this has the implication that for sufficiently small ε> 0, for all n, any marking of an ε fraction of the vertices of the ndimensional hypercube necessarily leaves a vertex x such that marked vertices are a
Extraconnectivity of hypercubes (II)
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 47 (2010), PAGES 189–195
, 2010
"... The gextraconnectivity κg(G) of a simple connected graph G is the minimum cardinality of a subset of V (G), if any, whose deletion disconnects G in such a way that every remaining component has at least g vertices. In this paper, we determine κg(Qn) for n +2 ≤ g ≤ 2n, n ≥ 4, where Qn denotes the n ..."
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Cited by 1 (0 self)
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The gextraconnectivity κg(G) of a simple connected graph G is the minimum cardinality of a subset of V (G), if any, whose deletion disconnects G in such a way that every remaining component has at least g vertices. In this paper, we determine κg(Qn) for n +2 ≤ g ≤ 2n, n ≥ 4, where Qn denotes the ndimensional
On 2detour subgraphs of the hypercube
"... Abstract. A spanning subgraph H of a graph G is a 2detour subgraph of G if for each x,y ∈ V (G), dH(x,y) ≤ dG(x,y) + 2. We prove a conjecture of Erdős, Hamburger, Pippert, and Weakley by showing that for some positive constant c and every n, each 2detour subgraph of the ndimensional hypercube Qn ..."
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Abstract. A spanning subgraph H of a graph G is a 2detour subgraph of G if for each x,y ∈ V (G), dH(x,y) ≤ dG(x,y) + 2. We prove a conjecture of Erdős, Hamburger, Pippert, and Weakley by showing that for some positive constant c and every n, each 2detour subgraph of the ndimensional hypercube
Results 1  10
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373