36750669
A minimum broadcast graph on 26 vertices
Broadcasting is the process of information dissemination in a communication network in which a message, originated by one member, is transmitted to all members of the network. A broadcast graph is a graph which permits broadcasting from any originator in minimum time. The broadcast function B(n) is the minimum number of edges in any broadcast graph on n vertices. In this paper, we construct a broadcast graph on 26 vertices with 42 edges to prove B(26) = 42.
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.
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.
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.
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].
15445426
An Ore-type Condition for Cyclability
A graph G is said to be cyclable if for each orientation D of G, there exists a set S(D) ?V(G) such that reversing all the arcs with one end in S results in a Hamiltonian digraph. Let G be a simple graph of even ordern? 8. In this paper, we show that if the degree sum of any two nonadjacent vertices is not less thann+ 1, then G is cyclable and the lower bound is sharp.
45668969
Efficient application migration under compiler guidance
2052176
Structural matching and discovery in document databases
Structural matching and discovery in documents such as SGML and HTML is important for data warehousing [6], version management [7, 11], hypertext authoring, digital libraries [4] and Internet databases. As an example, a user of the World Wide Web may be interested in knowing changes in an HTML document [2, 5, 10]. Such changes can be detected by comparing the old and new version of the document (referred to as structural matching of documents). As another example, in hypertext authoring, a user may wish to find the common portions in the history list of a document or in a database of documents (referred to as structural discovery of documents). In SIGMOD 95 demo sessions, we exhibited a software package, called TreeDiff [13], for comparing two latex documents and showing their differences. Given two documents, the tool represents the documents as ordered labeled trees and finds an optimal sequence of edit operations to transform one document (tree) to the other. An edit operation could be an insert, delete, or change of a node in the trees. The tool is so named because documents are represented and compared using approximate tree matching techniques [9, 12, 14].
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.
901722
Dynamic programming algorithms for haplotype block partitioning: applications to human chromosome 21 haplotype data
Recent studies have shown that the human genome has a haplotype block structure such that it can be divided into discrete blocks of limited haplotype diversity. Patil et al. [6] and Zhang et al. [12] developed algorithms to partition haplotypes into blocks with minimum number of tag SNPs for the entire chromosome. However, it is not clear how to partition haplotypes into blocks with restricted number of SNPs when only limited resources are available. In this paper, we first formulated this problem as finding a block partition with a fixed number of tag SNPs that can cover the maximal percentage of a genome. Then we solved it by two dynamic programming algorithms, which are fairly flexible to take into account the knowledge of functional polymorphism. We applied our algorithms to the published SNP data of human chromosome 21 combining with the functional information of these SNPs and demonstrated the effectiveness of them. Statistical investigation of the relationship between the starting points of a block partition and the coding and non-coding regions illuminated that the SNPs at these starting points are not significantly enriched in coding regions. We also developed an efficient algorithm to find all possible long local maximal haplotypes across a subset of samples. After applying this algorithm to the human chromosome 21 haplotype data, we found that samples with long local haplotypes are not necessarily globally similar.
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