206858561
Hamiltonian Cycles in Almost Claw-Free Graphs
Abstract. Some known results on claw-free graphs are generalized to the larger class of almost claw-free graphs. In this paper, we prove the following two results and conjecture that every 5-connected almost claw-free graph is hamiltonian. (1). Every 2-connected almost claw-free graph G∉J on n≤ 4 δ vertices is hamiltonian, where J is the set of all graphs defined as follows: any graph G in J can be decomposed into three disjoint connected subgraphs G1, G2 and G3 such that EG(Gi, Gj) = {ui, uj, vivj} for i≠j and i,j = 1, 2, 3 (where ui≠vi∈V(Gi) for i = 1, 2, 3). Moreover the bound 4δ is best possible, thereby fully generalizing several previous results. (2). Every 3-connected almost claw-free graph on at most 5δ−5 vertices is hamiltonian, hereby fully generalizing the corresponding result on claw-free graphs.
5906681
Circumferences of 2-Connected Claw-Free Graphs
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.
4909789
On Pancyclic Claw-Free Graphs
29060290
Hamiltonian Cycles in N2-Locally Connected Claw-Free Graphs
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.
32091631
K One-Way Heads Cannot Do String-Matching
We settle a conjecture raised by Z. Galil and J. Seiferas 14 years ago (J. Comput. System Sci.26(1983), 280?294):k-head one-way deterministic finite automata cannot perform string-machine (i.e., accept the language {x#y??u?vy=uxv}), for anyknonsensing heads.
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.
879315
Kolmogorov Random Graphs and the Incompressibility Method
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are (i) the mean and variance of the number of (possibly overlapping) ordered labeled subgraphs of a labeled graph as a function of its randomness deficiency (how far it falls short of the maximum possible Kolmogorov complexity) and (ii) a new elementary proof for the number of unlabeled graphs.
34458462
Learning in the Presence of Malicious Errors
In this paper an extension of the distribution-free model of learning introduced by Valiant [Comm. ACM, 27(1984), pp. 1134–1142] that allows the presence of malicious errors in the examples given to a learning algorithm is studied. Such errors are generated by an adversary with unbounded computational power and access to the entire history of the learning algorithm’s computation. Thus, a worst-case model of errors is studied.The results of this research include general methods for bounding the rate of error tolerable by any learning algorithm, efficient algorithms tolerating nontrivial rates of malicious errors, and equivalences between problems of learning with errors and standard combinatorial optimization problems.
5393650
PaDDMAS: parallel and distributed data mining application suite
Discovering complex associations, anomalies and patterns in distributed data sets is gaining popularity in a range of scientific, medical and business applications. Various algorithms are employed to perform data analysis within a domain, and range from statistical to machine learning and AI based techniques. Several issues need to be addressed however to scale such approaches to large data sets, particularly when these are applied to data distributed at various sites. As new analysis techniques are identified, the core tool set must enable easy integration of such analytical components. Similarly, results from an analysis engines must be sharable, to enable storage, visualisation or further analysis of results. We describe the architecture of PaDDMAS, a component based system for developing distributed data mining applications. PaDDMAS provides a tool set for combining pre-developed or custom components using a dataflow approach, with components performing analysis, data extraction or data management and translation. Each component is wrapped as a Java/CORBA object, and has an interface defined in XML. Components can be serial or parallel objects, and may be binary or contain a more complex internal structure. We demonstrate a prototype using a neural network analysis algorithm.