Degree Conditions for Hamiltonian Properties of Claw-free Graphs

This thesis contains many new contributions to the field of hamiltonian graph theory, a very active subfield of graph theory. In particular, we have obtained new sufficient minimum degree and degree sum conditions to guarantee that the graphs satisfying these conditions, or their line graphs, admit a Hamilton cycle (or a Hamilton path), unless they have a small order or they belong to well-defined classes of exceptional graphs. Here, a Hamilton cycle corresponds to traversing the vertices and edges of the graph in such a way that all their vertices are visited exactly once, and we return to our starting vertex (similarly, a Hamilton path reflects a similar way of traversing the graph, but without the last restriction, so we might terminate at a different vertex). In Chapter 1, we presented an introduction to the topics of this thesis together with Ryjáček’s closure for claw-free graphs, Catlin’s reduction method, and the reduction of the core of a graph. In Chapter 2, we found the best possible bounds for the minimum degree condition and the minimum degree sums condition of adjacent vertices for traceability of 2-connected claw-free graph, respectively. In addition, we decreased these lower bounds with one family of well characterized exceptional graphs. In Chapter 3, we extended recent results about the conjecture of Benhocine et al. and results about the conjecture of Z.-H Chen and H.-J Lai. In Chapters 4, 5 and 6, we have successfully tried to unify and extend several existing results involving the degree and neighborhood conditions for the hamiltonicity and traceability of 2-connected claw-free graphs. Throughout this thesis, we have investigated the existence of Hamilton cycles and Hamilton paths under different types of degree and neighborhood conditions, including minimum degree conditions, minimum degree sum conditions on adjacent pairs of vertices, minimum degree sum conditions over all independent sets of t vertices of a graph, minimum cardinality conditions on the neighborhood union over all independent sets of t vertices of a graph, as well minimum cardinality conditions on the neighborhood union over all t vertex sets of a graph. Despite our new contributions, many problems and conjectures remain unsolved

Towards Automating the Construction & Maintenance of Attack Trees: a Feasibility Study

Security risk management can be applied on well-defined or existing systems; in this case, the objective is to identify existing vulnerabilities, assess the risks and provide for the adequate countermeasures. Security risk management can also be applied very early in the system's development life-cycle, when its architecture is still poorly defined; in this case, the objective is to positively influence the design work so as to produce a secure architecture from the start. The latter work is made difficult by the uncertainties on the architecture and the multiple round-trips required to keep the risk assessment study and the system architecture aligned. This is particularly true for very large projects running over many years. This paper addresses the issues raised by those risk assessment studies performed early in the system's development life-cycle. Based on industrial experience, it asserts that attack trees can help solve the human cognitive scalability issue related to securing those large, continuously-changing system-designs. However, big attack trees are difficult to build, and even more difficult to maintain. This paper therefore proposes a systematic approach to automate the construction and maintenance of such big attack trees, based on the system's operational and logical architectures, the system's traditional risk assessment study and a security knowledge database.Comment: In Proceedings GraMSec 2014, arXiv:1404.163

Why and How Your Traceability Should Evolve: Insights from an Automotive Supplier

Traceability is a key enabler of various activities in automotive software and systems engineering and required by several standards. However, most existing traceability management approaches do not consider that traceability is situated in constantly changing development contexts involving multiple stakeholders. Together with an automotive supplier, we analyzed how technology, business, and organizational factors raise the need for flexible traceability. We present how traceability can be evolved in the development lifecycle, from early elicitation of traceability needs to the implementation of mature traceability strategies. Moreover, we shed light on how traceability can be managed flexibly within an agile team and more formally when crossing team borders and organizational borders. Based on these insights, we present requirements for flexible tool solutions, supporting varying levels of data quality, change propagation, versioning, and organizational traceability.Comment: 9 pages, 3 figures, accepted in IEEE Softwar

On the Core of Multiple Longest Traveling Salesman Games

In this paper we introduce multiple longest traveling salesman (MLTS) games. An MLTS game arises from a network in which a salesman has to visit each node (player) precisely once, except its home location, in an order that maximizes the total reward.First it is shown that the value of a coalition of an MLTS game is determined by taking the maximum of suitable combinations of one and two person coalitions.Secondly it is shown that MLTS games with ¯ve or less players have a nonempty core.However, a six player MLTS game may have an empty core.For the special instance where the reward between a pair of nodes is equal to 0 or 1, we provide relations between the structure of the core and the underlying network.game theory;traveling salesman problem;games;core

Boundary Objects and their Use in Agile Systems Engineering

Agile methods are increasingly introduced in automotive companies in the attempt to become more efficient and flexible in the system development. The adoption of agile practices influences communication between stakeholders, but also makes companies rethink the management of artifacts and documentation like requirements, safety compliance documents, and architecture models. Practitioners aim to reduce irrelevant documentation, but face a lack of guidance to determine what artifacts are needed and how they should be managed. This paper presents artifacts, challenges, guidelines, and practices for the continuous management of systems engineering artifacts in automotive based on a theoretical and empirical understanding of the topic. In collaboration with 53 practitioners from six automotive companies, we conducted a design-science study involving interviews, a questionnaire, focus groups, and practical data analysis of a systems engineering tool. The guidelines suggest the distinction between artifacts that are shared among different actors in a company (boundary objects) and those that are used within a team (locally relevant artifacts). We propose an analysis approach to identify boundary objects and three practices to manage systems engineering artifacts in industry