204992426
Hamiltonian cycles in regular 3-connected claw-free graphs
Abstract A known result by the author in 1991 is that every 3-connected claw-free graph on at most 6δ-11 vertices is Hamiltonian. In this paper it is proved that every 3-connected k -regular claw-free graph on at most 7 k — 19 vertices is Hamiltonian.
30829488
Vertex pancyclism in claw-free graphs
Abstract In this paper, we show four sufficient conditions for vertex pancyclicity in claw-free graphs. These results improve, respectively, results of Broersma and Veldman, Gould and Jacobson, and Ryjacek. In particular, we prove that if G is a 3-connected claw-free graph such that the vertices of degree 1 of every induced bull have a common neighbor in G then every vertex of G is contained in a cycle of all possible lengths except for four and five. We conjecture that almost all pancyclic claw-free graphs with minimum degree at least three are vertex pancyclic.
41518374
Longest cycles in regular 2-connected claw-free graphs
In this paper, we show that every 2-connected, k-regular claw-free graph on n vertices contains a cycle of length at least min 4k?2, n (k?8), and this result is best possible.
29060290
Hamiltonian Cycles in N2-Locally Connected Claw-Free Graphs
5906681
Circumferences of 2-Connected Claw-Free Graphs
4909789
On Pancyclic Claw-Free Graphs
3009418
The hamiltonian index of a graph and its branch-bonds
Let $G$ be an undirected and loopless finite graph that is not a path. The minimum $m$ such that the iterated line graph $L^m(G)$ is hamiltonian is called the hamiltonian index of $G,$ denoted by $h(G).$ A reduction method to determine the hamiltonian index of a graph $G$ with $h(G)\geq 2$ is given here. With it we will establish a sharp lower bound and a sharp upper bound for $h(G)$, respectively, which improves some known results of P.A. Catlin et al. [J. Graph Theory 14 (1990)] and H.-J. Lai [Discrete Mathematics 69 (1988)]. Examples show that $h(G)$ may reach all integers between the lower bound and the upper bound.
45224109
Service Matchmaking and Discovery with Rough Sets
The past few years have seen the Grid is evolving as a service-oriented computing infrastructure. It is foreseen that various resources in a Grid environment will be exposed as services for use by a wider user community. Service discovery becomes an issue of vital importance for utilising Grid facilities. This paper presents Rosse, a Rough Sets based Search Engine for service discovery that can deal with uncertainty of service properties when matching service advertisements with service requests. The evaluation results show that Rosse is more effective in service discovery compared with other mechanisms such as UDDI keyword matching and OWL-S matchmaking.
15883268
The expected size of Heilbronn's triangles
Heilbronn's triangle problem asks for the least /spl Delta/ such that n points lying in the unit disc necessarily contain a triangle of area at most /spl Delta/. Heilbronn initially conjectured /spl Delta/=O(1/n/sup 2/). As a result of concerted mathematical effort it is currently known that there are positive constants c and C such that c log n/n/sup 2//spl les//spl Delta//spl les/C/n/sup 8/7-/spl epsiv// for every constant /spl epsiv/>0. We resolve Heilbronn's problem in the expected case: If we uniformly at random put n points in the unit disc then (i) the area of the smallest triangle has expectation /spl Theta/(1/n/sup 3/); and (ii) the smallest triangle has area /spl Theta/(1/n/sup 3/) with probability almost one. Our proof uses the incompressibility method based on Kolmogorov complexity.
15861046
A Survey on Topology issues in Wireless Sensor Network
Topology issues have received more and more attentions in Wireless Sensor Networks (WSN). While WSN applications are normally optimized by the given underlying network topology, another trend is to optimize WSN by means of topology control. A number of approaches have been invested in this area, such as topology directed routing, cooperating schemes, sensor coverage based topology control and network connectivity based topology control. Most of the schemes have proven to be able to provide a better network monitoring and communication performance with prolonged system lifetime. In this survey paper, we provide a full view of the studies in this area. By summarizing previous achievements and analyzing existed problems, we also point out possible research directions for future work .
2607374
Information distance
While Kolmogorov complexity is the accepted absolute measure of information content in an individual finite object, a similarly absolute notion is needed for the information distance between two individual objects, for example, two pictures. We give several natural definitions of a universal information metric, based on length of shortest programs for either ordinary computations or reversible (dissipationless) computations. It turns out that these definitions are equivalent up to an additive logarithmic term. We show that the information distance is a universal cognitive similarity distance. We investigate the maximal correlation of the shortest programs involved, the maximal uncorrelation of programs (a generalization of the Slepian–Wolf theorem of classical information theory), and the density properties of the discrete metric spaces induced by the information distances. A related distance measures the amount of nonreversibility of a computation. Using the physical theory of reversible computation, we give an appropriate (universal, antisymmetric, and transitive) measure of the thermodynamic work required to transform one object in another object by the most efficient process. Information distance between individual objects is needed in pattern recognition where one wants to express effective notions of “pattern similarity” or “cognitive similarity” between individual objects and in thermodynamics of computation where one wants to analyze the energy dissipation of a computation from a particular input to a particular output.