P\'osa-type results for Berge-hypergraphs

A Berge cycle of length $k$ in a hypergraph $\mathcal H$ is a sequence of distinct vertices and hyperedges $v_1,h_1,v_2,h_2,\dots,v_{k},h_k$ such that $v_{i},v_{i+1}\in h_i$ for all $i\in[k]$, indices taken modulo $k$. F\"uredi, Kostochka and Luo recently gave sharp Dirac-type minimum degree conditions that force non-uniform hypergraphs to have Hamiltonian Berge cycles. We give a sharp P\'osa-type lower bound for $r$-uniform and non-uniform hypergraphs that force Hamiltonian Berge cycles

Ramsey numbers of Berge-hypergraphs and related structures

For a graph $G=(V,E)$, a hypergraph $\mathcal{H}$ is called a Berge-$G$, denoted by $BG$, if there exists a bijection $f: E(G) \to E(\mathcal{H})$ such that for every $e \in E(G)$, $e \subseteq f(e)$. Let the Ramsey number $R^r(BG,BG)$ be the smallest integer $n$ such that for any $2$-edge-coloring of a complete $r$-uniform hypergraph on $n$ vertices, there is a monochromatic Berge-$G$ subhypergraph. In this paper, we show that the 2-color Ramsey number of Berge cliques is linear. In particular, we show that $R^3(BK_s, BK_t) = s+t-3$ for $s,t \geq 4$ and $\max(s,t) \geq 5$ where $BK_n$ is a Berge-$K_n$ hypergraph. For higher uniformity, we show that $R^4(BK_t, BK_t) = t+1$ for $t\geq 6$ and $R^k(BK_t, BK_t)=t$ for $k \geq 5$ and $t$ sufficiently large. We also investigate the Ramsey number of trace hypergraphs, suspension hypergraphs and expansion hypergraphs.Comment: Updated to include suggestions of the refere

The maximum number of PℓP_\ell copies in PkP_k-free graphs

Generalizing Tur\'an's classical extremal problem, Alon and Shikhelman investigated the problem of maximizing the number of $T$ copies in an $H$-free graph, for a pair of graphs $T$ and $H$. Whereas Alon and Shikhelman were primarily interested in determining the order of magnitude for large classes of graphs $H$, we focus on the case when $T$ and $H$ are paths, where we find asymptotic and in some cases exact results. We also consider other structures like stars and the set of cycles of length at least $k$, where we derive asymptotically sharp estimates. Our results generalize well-known extremal theorems of Erd\H{o}s and Gallai

ქართული ევროპიული მოძრაობა

1950-იანი წლების დასაწყისშიევროპის ქვეყნების გამაერთი­ანებელი მოძრაობის დაწყებას სიხარულით შეხვდნენ ქართულ პო­ლიტიკურ ემიგრაციაში და მას საქართველოს მომავალი დაუკავში­რეს. 1952 წლის ნოემბერში ჟურნალმა „ბედი ქართლისა:“ გამოაქვეყ­ნა კალისტრატე სალიას (1901-1986) წერილი „ქართული ევროპი­ული მოძრაობა“, რომელშიც მიესალმება ამ სახელწოდების მოძრა­ობის შექმნას და განიხილავს საქართველოს ისტორიულ კავშირს ევროპულ ცივილიზაციასთან. „ევროპული ქართული მოძრაობა“ ოფიციალურად დაარსდა 1952 წლის აგვისტოში

An Econometric Assessment of Entrepreneurship in the Diamond Mining Sector and Its Impact on Economic Growth in Sierra Leone

This study examines the relationship between entrepreneurship in the diamond mining sector and economic growth in Sierra Leone for the period 1970-2013. The neoclassical production function is employed to explore new firm formation in the mining sector as a separate determinant of economic growth. Using recent econometric technique, the study finds a unique co-integrating relationship among real GDP, entrepreneurship, labour and capital. The results suggest that entrepreneurship exerts a positive and statistically significant effect on economic growth, and investment in the diamond mining sector is an important channel through which entrepreneurs fuel economic growth. Policy recommendation calls for entrepreneurship education, improving on the general labour capacity, facilitating access to finance, improving support services and the employment conditions for entrepreneurship. Keywords: Entrepreneurship, diamond sector, economic growth, co-integration, Sierra Leone DOI: 10.7176/RHSS/9-7-05 Publication date: April 30th 201

Analysis of the Impact of Social Marketing on the Reduction of Seroprevalence of Infection in Mali: Case of the NGO Wale in the Urban Commune of Ségou

This work aims to assess the importance of social marketing through communication in reducing the seroprevalence of HIV infection in the urban commune of Ségou. This analysis, based on both theoretical and empirical studies, involved a sample of one hundred and five (100) people made up of residents of the urban commune of Ségou and staff of the NGO Walé.  The results of our research "The impact of social marketing on reducing hiv infection in Mali" show that the majority of respondents in the urban commune of Ségou (81%) are satisfied with the means of communication of social marketing to reduce the seroprevalence of HIV infection against 19% of unsusc satisfied for various reasons (4% due to the always high rate, 9% of cases of denial and 6% who find communication strategies insufficient).Of 81% of people who are satisfied with the means of social marketing communication used to reduce the seroprevalence of HIV/AIDS, 49% are men compared to 32% of women.  Our results show that the use of social marketing techniques has a positive impact on the reduction of seroprevalence in the urban commune of Ségou. Keywords: social marketing, seroprevalence reduction, infection DOI: 10.7176/EJBM/12-36-03 Publication date: December 31st 202

The Impact of Microcredit on Promoting Female Entrepreneurship: The Case of the Cooperative of Women Merchants in the Municipality of Gao

This work is based on a questionnaire intended for women entrepreneurs in the municipality of Gao. This research therefore aims to measure the effect of microcredit on the development of income-generating activities for these women.It is based on a particular case, namely the impact of credit on the activities of traders in the commune of Gao. The methodology used for this research is the descriptive method which is based on a statistical analysis through graphs, and cross tables, with version 20 of the Statistical Package for the Social Sciences (SPSS) software and the R (4.2.1, our sample was made up of 100 women, all members of the cooperative of women traders in the commune of Gao.Our results indicate that microcredit has a positive effect on the income-generating activities of beneficiaries. Thus, women's access to this credit has enabled them to increase their turnover and their profits, while meeting the conditions for the sustainability of their income-generating activities through the strengthening of organizational capacities. Keywords: female entrepreneurship, micro credit, tradeswoman, multinomial logit. DOI: 10.7176/EJBM/14-24-01 Publication date: December 31st 202

3-uniform linear hypergraphs without a long Berge path

Extensions of the Erdős-Gallai theorem for general hypergraphs are well studied. In this work, we prove the extension of the Erdős-Gallai theorem for linear hypergraphs. In particular, we show that the number of hyperedges in an $n$-vertex $3$-uniform linear hypergraph, without a Berge path of length $k$ as a subgraph is at most $\frac{(k-1)}{6}n$ for $k\geq 4$. This is an extended abstract for EUROCOMB23 of the manuscript arXiv:2211.16184