206964202
Asymptotic Upper Bounds for Ramsey Functions
Abstract. We show that for any graph G with N vertices and average degree d, if the average degree of any neighborhood induced subgraph is at most a, then the independence number of G is at least Nfa+1(d), where fa+1(d)=∫01(((1−t)1/(a+1))/(a+1+(d−a−1)t))dt. Based on this result, we prove that for any fixed k and l, there holds r(Kk+l,Kn)≤ (l+o(1))nk/(logn)k−1. In particular, r(Kk, Kn)≤(1+o(1))nk−1/(log n)k−2.
43234278
A Ramsey Goodness Result for Graphs with Many Pendant Edges
2037433
An upper bound for ramsey numbers
Let G″ be a graph obtained from G by deleting two vertices. It is shown that r(G, H) ⩽ A + B + 2 + 2 (A2 + AB + B2)3 where A = r(G″, H) and B = r(G,H″).
17658871
On generalized Ramsey numbers
Abstract Let f 1 and f 2 be graph parameters. The Ramsey number r ( f 1 ⩾ m ; f 2 ⩾ n ) is defined as the minimum integer N such that any graph G on N vertices, either f 1 ( G )⩾ m or f 2 ( G )⩾n . A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t ( G ). We verify that (1−o(1))(24 n ) 1/3 ⩽ r ( t ⩾ n ; t ⩾ n )⩽(1+o(1))(48 n ) 1/3 as n →∞.
34644814
The Independence Number of Graphs with a Forbidden Cycle and Ramsey Numbers
Let k ≥ 5 be a fixed integer and let m = ⌊(k − 1)/2⌋. It is shown that the independence number of a Ck-free graph is at least c1[∑ d(v)1/(m − 1)](m − 1)/m and that, for odd k, the Ramsey number r(Ck, Kn) is at most c2(nm + 1/log n)1/m, where c1 = c1(m) > 0 and c2 = c2(m) > 0.
206570728
On Book-Complete Graph Ramsey Numbers
It is shown that a graph of orderNand average degreedthat does not contain the bookBm=K1+K1, mas a subgraph has independence number at leastNf(d), wheref(x)~(logx/x)(x?∞). From this result we find that the book-complete graph Ramsey number satisfiesr(Bm, Kn)?mn2/log(n/e). It is also shown that for every treeTmwithmedges,r(K1+Tm,Kn)?(2m?1)n2/log(n/e).
7190108
NaLIX: an interactive natural language interface for querying XML
Database query languages can be intimidating to the non-expert, leading to the immense recent popularity for keyword based search in spite of its significant limitations. The holy grail has been the development of a natural language query interface. We present NaLIX, a generic interactive natural language query interface to an XML database. Our system can accept an arbitrary English language sentence as query input, which can include aggregation, nesting, and value joins, among other things. This query is translated, potentially after reformulation, into an XQuery expression that can be evaluated against an XML database. The translation is done through mapping grammatical proximity of natural language parsed tokens to proximity of corresponding elements in the result XML. In this demonstration, we show that NaLIX, while far from being able to pass the Turing test, is perfectly usable in practice, and able to handle even quite complex queries in a variety of application domains. In addition, we also demonstrate how carefully designed features in NaLIX facilitate the interactive query process and improve the usability of the interface.
24660543
A note on the lower bounds of signed domination number of a graph
Abstract Let G = (V, E) be a graph. For a function f : V → {−1, 1}, the weight of f is w(f) = Σv ∈ V f(v). For a vertex v in V, we define f[v] = Σu∈N[v] f(u). A signed dominating function of G is a function f : V → {−1, 1} such that f[v] ⩾ 1 for all v ∈ V. The signed domination number γs(G) of G is the minimum weight of a signed dominating function on G. A signed dominating function of a weight γs(G) we call a γs-function of G. In this paper, we study the signed domination problem of general graph, and obtain some lower bounds of the signed domination number of a graph, and show that these lower bounds are sharp, and extend a result in Dunbar et al. (1995).
7038620
Practical inference control for data cubes
The fundamental problem for inference control in data cubes is how to efficiently calculate the lower and upper bounds for each cell value given the aggregations of cell values over multiple dimensions. In this paper, we provide the first practical solution for estimating exact bounds in two-dimensional irregular data cubes (i.e., data cubes in which certain cell values are known to a snooper). Our results imply that the exact bounds cannot be obtained by a direct application of the Frechet bounds in some cases. We then propose a new approach to improve the classic Frechet bounds for any high-dimensional data cube in the most general case. The proposed approach improves upon the Frechet bounds in the sense that it gives bounds that are at least as tight as those computed by Frechet, yet is simpler in terms of time complexity. Based on our solutions to the fundamental problem, we discuss two security applications, privacy protection of released data and fine-grained access control and auditing
6040880
Rupture degree of graphs
We introduce a new graph parameter, the rupture degree. The rupture degree for a complete graph K n is defined as 1−n, and the rupture degree for an incomplete connected graph G is defined by r(G)=max{ω(G−X)−|X|−m(G−X):X⊂V(G), ω(G−X)>1}, where ω(G−X) is the number of components of G−X and m(G−X) is the order of a largest component of G−X. It is shown that this parameter can be used to measure the vulnerability of networks. Rupture degrees of several specific classes of graphs are determined. Formulas for the rupture degree of join graphs and some bounds of the rupture degree are given. We also obtain some Nordhaus–Gaddum type results for the rupture degree.
26456568
Disclosure Analysis for Two-Way Contingency Tables
Disclosure analysis in two-way contingency tables is important in categorical data analysis. The disclosure analysis concerns whether a data snooper can infer any protected cell values, which contain privacy sensitive information, from available marginal totals (i.e., row sums and column sums) in a two-way contingency table. Previous research has been targeted on this problem from various perspectives. However, there is a lack of systematic definitions on the disclosure of cell values. Also, no previous study has been focused on the distribution of the cells that are subject to various types of disclosure. In this paper, we define four types of possible disclosure based on the exact upper bound and/or the lower bound of each cell that can be computed from the marginal totals. For each type of disclosure, we discover the distribution pattern of the cells subject to disclosure. Based on the distribution patterns discovered, we can speed up the search for all cells subject to disclosure.