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We consider a canonical Ramsey type problem. An edge-coloring of a graph is called m-good if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f (m, G) denote the smallest n such that every m-good edge-coloring of K n yields a properly edge-colored copy of G, and let g(m, G) denote the smallest n such that(More)
Given a graph G and a subset W ⊆ V (G), a Steiner W-tree is a tree of minimum order that contains all of W. Let S(W) denote the set of all vertices in G that lie on some Steiner W-tree; we call S(W) the Steiner interval of W. If S(W) = V (G), then we call W a Steiner set of G. The minimum order of a Steiner set of G is called the Steiner number of G. Given(More)
Given positive integers n and d, let A/sub 2/(n,d) denote the maximum size of a binary code of length n and minimum distance d. The well-known Gilbert-Varshamov bound asserts that A/sub 2/(n,d)/spl ges/2/sup n//V(n,d-l), where V(n,d) = /spl sigma//sub i=0//sup d/(/sub i//sup n/) is the volume of a Hamming sphere of radius d. We show that, in fact, there(More)
Given two graphs G and H, let f (G,H) denote the minimum integer n such that in every coloring of the edges of K n , there is either a copy of G with all edges having the same color or a copy of H with all edges having different colors. We show that f (G,H) is finite iff G is a star or H is acyclic. If S and T are trees with s and t edges, respectively, we(More)
The paper provides an account on the augmentation of a Chinese-English patent parallel corpus consisting of about 160K sentence pairs, which has been enlarged by about 45 times to more than 7 million sentence pairs mostly by the means of " harvesting " comparable patents from the Web. First, based on a large corpus of English-Chinese comparable patents,(More)
A d-simplex is a collection of d + 1 sets such that every d of them have nonempty intersection and the intersection of all of them is empty. A strong d-simplex is a collection of d + 2 sets A, A A d+1 } is a d-simplex, while A contains an element of ∩ j =i A j 454] conjectured that if k ≥ d + 1 ≥ 3, n > k(d + 1)/d, and F is a family of k-element subsets of(More)