The Max-Flow Min-Cut Theorem for Countable Networks

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are "orthogonal" to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.Comment: 19 pages, to be published in Journal of Combinatorial Theory, Series

Relation between start-ups’ online social media presence and fundraising

Purpose: The purpose of this study is to examine the emergences of social media such as Facebook, Twitter and Instagram have changed the way human beings communicate and interact. In the past few years, this has become crucial in the context of business, especially in start-up fund raising. Access to venture capital financing is a crucial issue in the entrepreneurial finance literature. To further explore the use of social media for entrepreneurs, the authors have explored how entrepreneurs use social media for fund-raising purposes. The authors have used Application Programming Interfaces (APIs) to collect entrepreneurs’ funding data from Crunchbase and entrepreneurs’ social media data from Facebook and Twitter. The results show that social media is significant for start-ups in their success or failure in fund raising. Investing energy into utilizing online social media and exhausting these platforms consciously contributes to the financial success of start-ups. Therefore, start-ups which are popular among online fans and followers can manage to raise larger amounts of funding in the early stages. Design/methodology/approach: This research relies on a wide range of quantitative data, which was obtained from three different online sources which includes Facebook, Twitter and CrunchBase. The use of a variety of internet technologies have been linked to increases in individuals’ social network diversity, which likely increases access to social capital at the individual level (Hampton and Wellman, 2003). The dataset was retrieved by using APIs, which enables the collection of novel metrics, from various sources that provide a well-structured dataset (Priem and Hemminger, 2010). Hypotheses were tested on a longitudinal dataset from 2000 to 2013, comprising general and investment data and social media metrics of start-ups. First, a sample from the database was selected to ensure data availability and reliability. After sampling, all the selected companies’ Twitter and Facebook activities were observed and metrics were analysed. SPSS was used to conduct correlation and regression analyses. Findings: This study analysed whether start-ups’ social media convention is able to influence investors’ choices, especially the amount of total funding given. The paper showed that innovative start-up companies were able to benefit from communicating on social media platforms. Start-ups, which were using Facebook and Twitter effectively, focusing on valuable social media metrics, received larger amount of funding in total. Furthermore, it was observed that as their business grew, they intended to put more effort into online social networking. It confirmed the idea that businesses are using social media consciously. Originality/value: This is the only paper that the authors could find that examines the relationship between fundraising and activity on social networks

Cliques in the union of graphs

Let B and R be two simple graphs with vertex set V, and let G(B, R) be the simple graph with vertex set V, in which two vertices are adjacent if they are adjacent in at least one of Band R. For X⊆V, we denote by B|X the subgraph of B induced by X; let R|X and G(B, R)|X be defined similarly. A clique in a graph is a set of pairwise adjacent vertices. A subset U⊆V is obedient if U is the union of a clique of B and a clique of R. Our first result is that if B has no induced cycles of length four, and R has no induced cycles of length four or five, then every clique of G(B, R)is obedient. This strengthens a previous result of the second author, stating the same when B has no induced C_4 and R is chordal. The clique number of a graph is the size of its maximum clique. We say that the pair (B, R)is additive if for every X⊆V, the sum of the clique numbers of B|X and R|X is at least the clique number of G(B, R)|X. Our second result is a sufficient condition for additivity of pairs of graphs

The Role of Private Label Brands in Enhancing Service Satisfaction in the Hotel Industry: Comparing Luxury and Boutique Hotels

This research proposes private label branding as a strategy that can have a positive effect on guest satisfaction and loyalty in hotels that cater to travelers seeking a special hotel experience. We test this using the well-established SERVQUAL model of service quality, based on a sample of guests in two hotels: a five-star luxury hotel (N=225) and a boutique hotel (N=101). The findings show that in the luxury hotel but not the boutique hotel, perception of a private label had a direct impact on loyalty, and an indirect impact on loyalty through its effect on guest satisfaction. The theoretical implications and recommendations for hoteliers based on the findings are discussed

The evolution of management from a trust to arm’s length model in family run businesses: the case of the diamond industry

Purpose: The primary purpose of this paper is to fill the research gap regarding the evolution of managerial processes within (largely family) diamond industry firms, especially over the past seven decades. Design/methodology/approach: Qualitative data were gathered from interviews with 100 managers in the diamond industry in Israel, together with data from Israeli Government, industry and academic sources. Findings: Over the recent life cycle of the diamond industry, with its changing structures and dynamics, participant firms have evolved through seven stages of engagement, from one based on trust and personal connections to more impersonal, standardized connections that exist today. Research limitations/implications: In seeking to tell the story of industry participants as a group, the differences in behaviours between the family firms and the non-family firms have not explored. This should be the work of future research, which, if aimed at teasing out the results of this study, may help shed additional light on the strategic processes that occur within family firms. Practical implications: Although the firms examined in this study were from one industry (and an arguably narrow cultural base), their development over time was not dissimilar to the experience reported in other industries and cultures. This suggests that the components of the evolution of the strategic process that ensues within family firms may be generalizable throughout cultures. In the absence of kin relationships, the importance of trust in their dealings cannot be overstated. Originality/value: The findings demonstrate how one group of participants in the global diamond industry has responded to the changing economic, social and political contexts of their operations, where trust and personal connections have been replaced by more impersonal, standardized dealings

Doing favors in the Arab world

The purpose of this paper is to analyze the role of Wasta, a culturally based system of social networks of exchange among in-group members in the Arab world, as exemplified by three groups of Arabs in the Palestinian Authority, and then compares it to Guanxi (China), Sviazi (Russia) and Jaan–Pechaan (India). The use of social networks is a common business model around the world to accomplish business objectives and is especially relied upon in emerging economies where formal institutions are weak. It is important to understand the commonalities and differences in the use of reciprocity in various cultural contexts in order to conduct business effectively. The aim of the paper is to illustrate the structure of Wasta and how it is perceived and constructed among three Arab social groups, and then compare and contrast it with social business models in three other high context cultures