37612124
Minimally circular-imperfect graphs with a major vertex
In this note, we characterize the minimally circular-imperfect graphs that have a major vertex.
20988039
Two conjectures equivalent to the perfect graph conjecture
Abstract In this note, we study the graphs with the property that each of their induced subgraphs has circular clique number (defined in Section 2) the same as its clique number, prove that a graph satisfies such a property if and only if neither itself nor its complement contains an induced subgraph isomorphic to an odd cycle of length at least five, and then give two conjectures which are equivalent to the perfect graph conjecture.
37647794
On 3-colorable plane graphs without 5- and 7-cycles
In this note, it is proved that every plane graph without 5- and 7-cycles and without adjacent triangles is 3-colorable. This improves the result of [O.V. Borodin, A.N. Glebov, A. Raspaud, M.R. Salavatipour, Planar graphs without cycles of length from 4 to 7 are 3-colorable, J. Combin. Theory Ser. B 93 (2005) 303-311], and offers a partial solution for a conjecture of Borodin and Raspaud [O.V. Borodin, A. Raspaud, A sufficient condition for planar graphs to be 3-colorable, J. Combin. Theory Ser. B 88 (2003) 17-27].
30641096
On the fixed edge of planar graphs with minimum degree five
Abstract An edge e of a finite and simple graph G is called a fixed edge of G if G - e + e ′ ≅ G implies e ′ = e . In this paper, we show that planar graphs with minimum degree 5 contain fixed edges, from which we prove that a class of planar graphs with minimum degree one is edge reconstructible.
12925025
The 4-Choosability of Plane Graphs without 4-Cycles'
A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosable.
7708894
Decomposing toroidal graphs into circuits and edges
Erdos et al. (Canad. J. Math. 18 (1966) 106-112) conjecture that there exists a constant d"c"e such that every simple graph on n vertices can be decomposed into at most d"c"en circuits and edges. We consider toroidal graphs, where the graphs can be embedded on the torus, and give a polynomial time algorithm to decompose the edge set of an even toroidal graph on n vertices into at most (n+3)/2 circuits. As a corollary, we get a polynomial time algorithm to decompose the edge set of a toroidal graph (not necessarily even) on n vertices into at most 3(n-1)/2 circuits and edges. This settles the conjecture for toroidal graphs.
31739418
Geometric Algorithms for Density-based Data Clustering
Data clustering is a fundamental problem arising in many practical applications. In this paper, we present new geometric approximation and exact algorithms for the density-based data clustering problem in d-dimensional space ℝd (for any constant integer d ≥ 2). Previously known algorithms for this problem are efficient only when the specified range around each input point, called the δ-neighborhood, contains on average a constant number of input points. Different distributions of the input data points have significant impact on the efficiency of these algorithms. In the worst case when the data points are highly clustered, these algorithms run in quadratic time, although such situations might not occur very frequently on real data. By using computational geometry techniques, we develop faster approximation and exact algorithms for the density-based data clustering problem in ℝd. In particular, our approximation algorithm based on the ∊-fuzzy distance function takes O(n log n) time for any given fixed value ∊>0, and our exact algorithms take sub-quadratic time. The running times and output quality of our algorithms do not depend on any particular data distribution. We believe that our fast approximation algorithm is of considerable practical importance, while our sub-quadratic exact algorithms are more of theoretical interest. We implemented our approximation algorithm and the experimental results show that our approximation algorithm is efficient on arbitrary input point sets.
34666787
Applying Agent into Web Testing and Evolution
Automatic Web testing and evolution is an effective method to ensure the quality of Web applications. In this paper, we apply Agent into this area, i.e. firstly, we explain the necessity and feasibility, and also give the general description of our method; then, we apply Agent into the Web performance testing, Web regression testing and Web usability evolution; conclusion remarks are given at last.
6156170
On edge domination numbers of graphs
Let @c"s^'(G) and @c"s"s^'(G) be the signed edge domination number and signed star domination number of G, respectively. We prove that 2n-4>[email protected]"s"s^'(G)>[email protected]"s^'(G)>=n-m holds for all graphs G without isolated vertices, where n=|V(G)|>=4 and m=|E(G)|, and pose some problems and conjectures.
30598486
Regression testing for Web applications based on slicing
Web applications have rapid developing speed and changeable user demands, so the regression testing is much important. Since the changed demands result in different versions of Web applications, and the faults usually hiding in the adjusted contents, the regression testing must cover all the related pages. In order to carry through the regression testing quickly and effectively, we make the simplification with the method of slicing. Firstly, we analyze the possible changes in the Web applications and the influences produced by these changes, discussing in the direct-dependent and indirect-dependent way; next, we give the regression testing method based on slicing emphasized on the indirect-dependent among data, i.e., obtaining the dependent set of changed variables by forward and backward search method and generating the testing suits; conclusion remarks and future work are given at last.
31788400
Extremal graphs for inequalities involving domination parameters
Abstract A characterization of n-vertex isolate-free connected graphs G whose domination number γ ( G ) satisfies γ(G)=⌊n/2⌋ is obtained. This result enables us to obtain extremal graphs of inequalities which bound the sum of two domination parameters in isolate-free graphs.