Asymmetric Ramsey properties of random graphs involving cliques and cycles

We prove that for every ℓ, r ≥ 3, there exists c > 0 such that for (image found), with high probability there is a 2-edge-colouring of the random graph Gn,p with no monochromatic copy of Kr of the first colour and no monochromatic copy of Cℓ of the second colour. This is a progress on a conjecture of Kohayakawa and Kreuter

Ramsey equivalence of Kn and Kn + Kn−1

We prove that, for n ≥ 4, the graphs Kn and Kn + Kn−1 are Ramsey equivalent. That is, if G is such that any red-blue colouring of its edges creates a monochromatic Kn then it must also possess a monochromatic Kn + Kn−1. This resolves a conjecture of Szabó, Zumstein, and Zürcher [10]. The result is tight in two directions. Firstly, it is known that Kn is not Ramsey equivalent to Kn + 2Kn−1. Secondly, K3 is not Ramsey equivalent to K3 + K2. We prove that any graph which witnesses this non-equivalence must contain K6 as a subgraph.</p

An approximate version of Jackson's conjecture

A diregular bipartite tournament is a balanced complete bipartite graph whose edges are oriented so that every vertex has the same in- and out-degree. In 1981 Jackson showed that a diregular bipartite tournament contains a Hamilton cycle, and conjectured that in fact its edge set can be partitioned into Hamilton cycles. We prove an approximate version of this conjecture: for every > 0 there exists n0 such that every diregular bipartite tournament on 2n ≥ n0 vertices contains a collection of (1/2-)n cycles of length at least (2-)n. Increasing the degree by a small proportion allows us to prove the existence of many Hamilton cycles: for every c > 1/2 and > 0 there exists n0 such that every cn-regular bipartite digraph on 2n ≥ n0 vertices contains (1)cn edge-disjoint Hamilton cycles

On minimal Ramsey graphs and Ramsey equivalence in multiple colours

For an integer q ≥ 2, a graph G is called q-Ramsey for a graph H if every q-colouring of the edges of G contains a monochromatic copy of H. If G is q-Ramsey for H yet no proper subgraph of G has this property, then G is called q-Ramsey-minimal for H. Generalizing a statement by Burr, Nešetil and Rödl from 1977, we prove that, for q ≥ 3, if G is a graph that is not q-Ramsey for some graph H, then G is contained as an induced subgraph in an infinite number of q-Ramsey-minimal graphs for H as long as H is 3-connected or isomorphic to the triangle. For such H, the following are some consequences.For 2 ≤ r < q, every r-Ramsey-minimal graph for H is contained as an induced subgraph in an infinite number of q-Ramsey-minimal graphs for H.For every q ≥ 3, there are q-Ramsey-minimal graphs for H of arbitrarily large maximum degree, genus and chromatic number.The collection Mq(H) H is 3-connected or K3 forms an antichain with respect to the subset relation, where Mq(H) denotes the set of all graphs that are q-Ramsey-minimal for H.We also address the question of which pairs of graphs satisfy Mq(H1)= Mq(H2) in which case H1 and H2 are called q-equivalent. We show that two graphs H1 and H2 are q-equivalent for even q if they are 2-equivalent, and that in general q-equivalence for some q ≥ 3 does not necessarily imply 2-equivalence. Finally we indicate that for connected graphs this implication may hold: Results by NešetÅ™il and Rödl and by Fox, Grinshpun, Liebenau, Person and Szabó imply that the complete graph is not 2-equivalent to any other connected graph. We prove that this is the case for an arbitrary number of colours

Internationalization and technological leapfrogging in the pharmaceutical industry

The pre-refereed author version of this article was published as a UNI-MERIT Working Paper under the title “Internationalising to create Firm Specific Advantages: Leapfrogging strategies of U.S. Pharmaceutical firms in the 1930s and 1940s & Indian Pharmaceutical firms in the 1990s and 2000s”. The paper can be downloaded from the UNU-MERIT website from the following link: http://arno.unimaas.nl/show.cgi?fid=12607.Internationalization is a useful strategy for gaining firm-specific technological advantages especially during periods of technological discontinuity as the pharmaceutical industry illustrates. The antibiotics revolution in the 1940s saw laggard US firms scrambling to gain capabilities in antibiotics. The possibilities of non-chemical routes to new drug discovery in the 1990s saw Indian generic drug manufacturers attempting to develop new drug discovery capabilities. This article compares the leapfrogging strategies adopted by US and Indian firms and shows that in both periods internationalization strategies were central to the technological strategies of both groups of firms

Privacy, identity and security concerns: enterprise strategic decision making and business model development for mobile payments in NFC

This paper assesses the privacy, identity and security concerns arising from the use of NFC (near field communications) technology in public transport systems. NFC is increasingly visible as the technology of choice for ticketing in public transport systems providing electronic and contactless payment. NFC is considered a disruptive technology competing with other alternative money payments, with innovative business propositions to both service providers and users. However, there are shortcomings and opportunities that arise from taking into account those aspects as part of the business models propositions for this technology. The case study is a comparative study of six cities around the work (London, Hong Kong, Helsinki, Berlin, Seoul and Tokyo), with particular focus on the variations of NFC public transport business model implementation. We pay particular attention to the enterprise strategic decisions taken by stakeholders resulting in a variety of business models in the access and usage of services. Some transport authorities prioritize revenue, others profit, others the expansion and consolidation of services. At the core of those decisions were mandates for the protection of citizens’ privacy, identity definition and security implementations which different levels of compliance and regulation. The demands that emerged from the regulatory aspects - or the lack of them - provide a dynamic set of alternatives that are used by stakeholders of the transport systems to develop their business models. We show how privacy and security default settings are adopted and later adjusted based on the demand of users and services. Our analytical model shows how this technology fosters diversity of business models. We analyze the stakeholders and the context on three layers: firstly, the architecture aspects related to the use of mobile technology, communication and transport networks, payment systems, services, etc.; secondly, the shareholder and public transport originators of the services; thirdly, the variety of rules and regulations for competition for the established forms of provision of services and the types of business solutions with variations driven to a strong private, state hybrid drive of business solutions. We show how this analysis fosters our understanding of the value chains for a technological innovation that is disruptive. We consider who are the winners and losers and especially assess the positions of network operators, since they so far have participated only tangentially in something that fundamentally depends upon their engagement. For users of NFC enabled transport systems, privacy is granted, in some cases, by current regulatory frameworks, but it is not properly embraced at the core of the current business models being implemented. This amounts to a loophole in regulation that will become critical in the future as NFC is extended to provide not only transport services but also other services such as banking. This research is novel in its approach to understanding the complexity of the strategic decisions taken by public transport operators by using a three element model. Our model considers the technology, the users and service providers, and the regulation and business models associated with privacy protection, identity definition and transactional security for NFC. We show how far this model can be transposed to other sectors that might be using NFC in the near future as well as discussing the potential policy and or regulatory rules to be implemented in order to provide a sustainable business environment which can also protect and nurture the privacy and identity of consumers