8284293
A note on list improper coloring planar graphs
A graph G is called (k, d)*-choosable if, for every list assignment L satisfying |L(v)| = k for all v ϵ V(G), there is an L-coloring of G such that each vertex of G has at most d neighbors colored with the same color as itself. In this note, we prove that every planar graph without 4-cycles and l-cycles for some l ϵ {5, 6, 7} is (3, 1)*-choosable.
29686713
A note on Ramsey numbers with two parameters
The Ramsey number R(G1, G2) is the smallest integer p such that for any graph G on p vertices either G contains G1 or G- contains G2, where G- denotes the complement of G. In this paper, some new bounds with two parameters for the Ramsey number R(G1, G2), under some assumptions, are obtained. Especially, we prove that R(K6 - e, K6) ≤ 116 and R(K6 - e, K7) ≤ 202, these improve the two upper bounds for the classical Ramsey number in [S.P. Radziszowski, Small Ramsey number, Electron. J. Combin. DSI (2002) 1-36].
30370540
On (d, 2)-dominating numbers of binary undirected de Bruijn graphs
Abstract In this paper, we show that: (i) For n-dimensional undirected binary de Bruijn graphs, UB(n), n⩾4, there is a vertex x=x 1 x 1 x 1 ⋯ x 1 x 1 (x1=1 or 0) such that for any other vertex t there exist at least two internally disjoint paths of length at most n−1 between x and t in UB(n), i.e., the (n−1,2)-dominating number of UB(n) is equal to one. (ii) For n⩾5, let S={100⋯01,011⋯10}. For any other vertex t there exist at least two internally disjoint paths of length at most n−2 between t and S in UB(n), i.e., the (n−2,2)-dominating number of UB(n) is no more than 2.
13354529
Edge-pancyclicity of coupled graphs
The coupled graph c(G) of a plane graph G is the graph defined on the vertex set V(G)∪F(G) so that two vertices in c(G) are joined by an edge if and only if they are adjacent or incident in G. We prove that the coupled graph of a 2-connected plane graph is edge-pancyclic. However, there exists a 2-edge-connected plane graph G such that c(G) is not Hamiltonian.
5672527
Complementary cycles containing a fixed arc in diregular bipartite tournaments
Abstract Let ( x , y ) be a specified arc in a k -regular bipartite tournament B . We prove that there exists a cycle C of length four through ( x , y ) in B such that B − C is hamiltonian.
14716028
New Upper Bounds for Ramsey Numbers
The Ramsey numberR(G1,G2) is the smallest integerpsuch that for any graphGonpvertices eitherGcontainsG1orGcontainsG2, whereGdenotes the complement ofG. LetR(m,n)=R(Km,Kn). Some new upper bound formulas are obtained forR(G1,G2andR(m,n), and we derive some new upper bounds for Ramsey numbers here.
8097819
Model Management Through Graph Transformation
Model management offers a higher level interface than current techniques for metadata management, and generic operators drastically reduce amount of programming for metadata applications. The interactive nature of generic model management operators inevitably demands an intuitive representation. This paper proposes a visual representation for model management operators based on graph transformation. Graph transformation formalisms, as the theoretic foundation of many visual programming languages, can formally represent model management operators by visual and intuitive expressions. By using graphical representations, users can easily comprehend and manipulate the operators and desired outputs
7869643
Fast parallel algorithms for the unit cost editing distance between trees
We present three algorithms to find the distance. The first algorithm is a simple dynamic programming algorithm based on a postorder traversal whose complexity improves upon the best previously published algorithm due to Tai (T79 in JACM). The second and third algorithms are parallel algorithms based on the application of suffix trees to the comparison problem. The cost of executing these algorithms is a monotonic increasing function of the distance between the two trees. Results Let trees T I and T2 have numbers of levels L i and L 2 respectively. Let k be the actual distance between T 1 and T2. Let N be rain (IT11, IT2 ]). The asymptotic running times (assuming a concurrentread concurrent-write parallel random access machine) are:
17536436
Combining visual and automated data mining for near-real-time anomaly detection and analysis in BGP
The security of Internet routing is a major concern because attacks and errors can result in data packets not reaching their intended destination and/or falling into the wrong hands. A key step in improving routing security is to analyze and understand it. In the past, we and other researchers have presented various visual-based, statistical-based, and signature-based methods of analyzing Internet routing data.
 In this paper, we describe an integration of visual and automated data mining methods for discovering and investigating anomalies in Internet routing. We show how these different components are combined in such a way as to complement each other, creating a very effective and useful analysis tool. In addition to performing analysis on archived data, our system is able to collect, process and visualize data in near-real-time.
1826127
On a Family-Based Haplotype Pattern Mining Method for Linkage Disequilibrium Mapping
Linkage disequilibrium mapping is an important tool in disease gene mapping. Recently, Toivonen et al. [1] introduced a haplotype mining (HPM) method that is applicable to data consisting of unrelated high-risk and normal haplotypes. The HPM method orders haplotypes by their strength of association with trait values, and uses all haplotypes exceeding a given threshold of strength of association to predict the gene location. In this study, we extend the HPM method to pedigree data by measuring the strength of association between a haplotype and quantitative traits of interest using the Quantitative Pedigree Disequilibrium Test proposed by Zhang et al. [2]. This family-based HPM (F-HPM) method can incorporate haplotype information across a set of markers and allow both missing marker data and ambiguous haplotype information. We use a simulation procedure to evaluate the statistical significance of the patterns identified from the F-HPM method. When the F-HPM method is applied to analyze the sequence data from the seven candidate genes in the simulated data sets in the 12th Genetic Analysis Workshop, the association between genes and traits can be detected with high power, and the estimated locations of the trait loci are close to the true sites.
52799334
On the Editing Distance Between Undirected Acyclic Graphs
We consider the problem of comparing CUAL graphs (Connected, Undirected, Acyclic graphs with nodes being Labeled). This problem is motivated by the study of information retrieval for bio-chemical and molecular databases. Suppose we define the distance between two CUAL graphs G1 and G2 to be the weighted number of edit operations (insert node, delete node and relabel node) to transform G1 to G2. By reduction from exact cover by 3-sets, one can show that finding the distance between two CUAL graphs is NP-complete. In view of the hardness of the problem, we propose a constrained distance metric, called the degree-2 distance, by requiring that any node to be inserted (deleted) have no more than 2 neighbors. With this metric, we present an efficient algorithm to solve the problem. The algorithm runs in time O(N1N2D2) for general weighting edit operations and in time for integral weighting edit operations, where Ni, i=1, 2, is the number of nodes in Gi, D=min{d1, d2} and di is the maximum degree of Gi.