Hypohamiltonian and almost hypohamiltonian graphs

This Dissertation is structured as follows. In Chapter 1, we give a short historical overview and define fundamental concepts. Chapter 2 contains a clear narrative of the progress made towards finding the smallest planar hypohamiltonian graph, with all of the necessary theoretical tools and techniques--especially Grinberg's Criterion. Consequences of this progress are distributed over all sections and form the leitmotif of this Dissertation. Chapter 2 also treats girth restrictions and hypohamiltonian graphs in the context of crossing numbers. Chapter 3 is a thorough discussion of the newly introduced almost hypohamiltonian graphs and their connection to hypohamiltonian graphs. Once more, the planar case plays an exceptional role. At the end of the chapter, we study almost hypotraceable graphs and Gallai's problem on longest paths. The latter leads to Chapter 4, wherein the connection between hypohamiltonicity and various problems related to longest paths and longest cycles are presented. Chapter 5 introduces and studies non-hamiltonian graphs in which every vertex-deleted subgraph is traceable, a class encompassing hypohamiltonian and hypotraceable graphs. We end with an outlook in Chapter 6, where we present a selection of open problems enriched with comments and partial results

Mobile Ad-Hoc Networks

Being infrastructure-less and without central administration control, wireless ad-hoc networking is playing a more and more important role in extending the coverage of traditional wireless infrastructure (cellular networks, wireless LAN, etc). This book includes state-of the-art techniques and solutions for wireless ad-hoc networks. It focuses on the following topics in ad-hoc networks: vehicular ad-hoc networks, security and caching, TCP in ad-hoc networks and emerging applications. It is targeted to provide network engineers and researchers with design guidelines for large scale wireless ad hoc networks

Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education

International audienceThis volume contains the Proceedings of the Seventh Congress of the European Society for Research in Mathematics Education (ERME), which took place 9-13 February 2011, at Rzeszñw in Poland