Supersaturation Problem for Color-Critical Graphs

The \emph{Tur\'an function} \ex(n,F) of a graph $F$ is the maximum number of edges in an $F$-free graph with $n$ vertices. The classical results of Tur\'an and Rademacher from 1941 led to the study of supersaturated graphs where the key question is to determine $h_F(n,q)$, the minimum number of copies of $F$ that a graph with $n$ vertices and \ex(n,F)+q edges can have. We determine $h_F(n,q)$ asymptotically when $F$ is \emph{color-critical} (that is, $F$ contains an edge whose deletion reduces its chromatic number) and $q=o(n^2)$. Determining the exact value of $h_F(n,q)$ seems rather difficult. For example, let $c_1$ be the limit superior of $q/n$ for which the extremal structures are obtained by adding some $q$ edges to a maximum $F$-free graph. The problem of determining $c_1$ for cliques was a well-known question of Erd\H os that was solved only decades later by Lov\'asz and Simonovits. Here we prove that $c_1>0$ for every {color-critical}~$F$. Our approach also allows us to determine $c_1$ for a number of graphs, including odd cycles, cliques with one edge removed, and complete bipartite graphs plus an edge.Comment: 27 pages, 2 figure

Complementarity between Irrigation and Fertilizer Technologies - A Justification for Increased Irrigation Investment in the Less-Favored Areas of SSA

There is a downward spiral of declining soil fertility, low crop yield and increasing poverty in the less-favored areas of SSA. The semi-arid tropics of northern Ghana share this episode. The soils in this part of the country are naturally less endowed, have little organic matter content and farmers use very little inorganic fertilizer. Existing studies indicate that the erratic nature of rainfall in the area increases risk and constrains farmers' investment on inorganic fertilizer. However, agronomic studies suggest that promotion of sustainable use of inorganic fertilizer is indispensable at least in the short to medium term to break the downward spiral. Therefore, promoting sustainable use of inorganic fertilizer use remains to be a policy challenge. This paper argues that in spite of observed disinvestment on irrigation both by governments and donors there is significant complementarity between irrigation and inorganic fertilizer use in the less-favored areas of northern Ghana. This implies that increased irrigation investment in the semi-arid tropics of SSA can be justified given its importance in reducing rainfall risk and boosting inorganic fertilizer use.Resource /Energy Economics and Policy, Q15, Q16, Q18,

Multiple Petersen subdivisions in permutation graphs

A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-connected, then every edge of M is contained in such a subdivision. Our proof is based on a characterization of cographs in terms of twin vertices. We infer a linear lower bound on the number of Petersen subdivisions in a permutation graph with no 4-cycles, and give a construction showing that this lower bound is tight up to a constant factor

The Erd\H{o}s-Rothschild problem on edge-colourings with forbidden monochromatic cliques

Let $\mathbf{k} := (k_1,\dots,k_s)$ be a sequence of natural numbers. For a graph $G$, let $F(G;\mathbf{k})$ denote the number of colourings of the edges of $G$ with colours $1,\dots,s$ such that, for every $c \in \{1,\dots,s\}$, the edges of colour $c$ contain no clique of order $k_c$. Write $F(n;\mathbf{k})$ to denote the maximum of $F(G;\mathbf{k})$ over all graphs $G$ on $n$ vertices. This problem was first considered by Erd\H{o}s and Rothschild in 1974, but it has been solved only for a very small number of non-trivial cases. We prove that, for every $\mathbf{k}$ and $n$, there is a complete multipartite graph $G$ on $n$ vertices with $F(G;\mathbf{k}) = F(n;\mathbf{k})$. Also, for every $\mathbf{k}$ we construct a finite optimisation problem whose maximum is equal to the limit of $\log_2 F(n;\mathbf{k})/{n\choose 2}$ as $n$ tends to infinity. Our final result is a stability theorem for complete multipartite graphs $G$, describing the asymptotic structure of such $G$ with $F(G;\mathbf{k}) = F(n;\mathbf{k}) \cdot 2^{o(n^2)}$ in terms of solutions to the optimisation problem.Comment: 16 pages, to appear in Math. Proc. Cambridge Phil. So

Coffee-Enset-Livestock Interaction for sustainable livelihood in the Sidama area of Southern Ethiopia

The coffee growing areas of Sidama, the midlands, are one of the densely populated areas in Ethiopia, with a population density of 500 persons per arable land. Coffee serves as the major cash source to the farm household, which expends the cash to its different uses one of which is asset formation through the purchase of livestock. Livestock of different type are reared with small herd size in the area. The population pressure brought land to be the most limiting production constraint. Due to its limitation the available land is mainly allocated to the major staple food of the area, Enset (Ensete ventricosum). This plant is everything to the farmer: food, feed, construction material etc. The food use of Enset is very significant, because it supports large population size, however it is deficient in fat, protein and energy. Enset covers the larger share of the feed use and it is a good feed sources because the feed part is rich in protein. This paper tried to address how the major enterprises of the system coffee, enset and livestock can be intensified so as to ensure sustainable livelihood in the farming system

Varieties Reaction for Wheat Rust Diseases in Hadiya Zone, Ethiopia

Wheat is an important cereal crop in Ethiopia that is widely cultivated in a wide range of altitude. It ranks fourth in area coverage and total production after teff, maize and sorghum. Hadiya Zone is one of the major wheat producing areas in Ethiopia and it is recognized as one of the wheat belts in the country. But wheat production is threatened by abiotic and biotic constraints. Among the biotic, wheat rust (stem rust, yellow rust and stripe rust) is one of the major limitations of wheat production. Even though, Hadiya zone is known in wheat production, there is no detailed information regarding the distribution, incidence and severity of wheat rust. Therefore, this study was conducted with the following objective: to assess the reaction of varieties against wheat rust. The survey was conducted in 2017main cropping season from mid September to mid October in three districts of Hadiya zone (Misha, Lemo and Duna). A total of 72 fields were surveyed at every 5 to 10 km using vehicle odometer along the main and accessible road sides. The plant samples with in a selected field were taken in X-fashion using 0.5m X 0.5m (0.25m2) quadrates. Reaction of wheat varieties to stem rust ranges from 5.5% - 16 %. The lowest severity of stem rust was recorded on variety Digalu (5.5%) where as the highest was from local variety (16%). In general, disease severity was classified under low class. The survey work showed that if susceptible improved and local cultivars continue to grow as mono-cropping system (due to strategy of cluster farming) serious wheat rust epidemics may occur in the zones and may cause high economic loss. Therefore, it is advised to device other farming system instead of cluster farming and replacing of susceptible varieties with new resistant varieties. DOI: 10.7176/JBAH/10-6-02 Publication date:March 31st 202

Determinants of University-Industry Linkage: Evidence from Dire Dawa City

It is recognized that the importance of linkage of higher education institutions with various industries for a given country sustainable development. However, in one or another way the linkage between universities and industries seems to be very weak particularly in developing countries. The aim of this study is to investigate factors that determine the University-Industry linkage in the case of Dire Dawa city. For the sake of achieving this objective, primary data was collected through structured questionnaire from a sample of 159 academicians that were selected using systematic random sampling techniques. Moreover, questionnaire was distributed to 31 companies that are selected using convenience sampling technique. Furthermore, interview for the focal person of Institute-Industry Technology Transfer office were conducted. While descriptive narrations through concurrent triangulation strategy were applied to analyze the data collected from interview, data collected using questionnaire were analyzed using descriptive statistics and econometric model (ordinal logistic regression). Hence, access of funding, previous experience and publication were found significant factors in determining University-Industry Linkage. The result of the study indicates that training and student internship programs are the two major areas where the university is collaborating with the industries. Thus, the university has to reform its incentive mechanism for researchers. Academicians should also have to conduct demand driven and quality researches to the industries in order to gain industries’ trust. Industrialists should support the academicians those who engaged in industry related tasks by offering financial and other supports. The Institute-Industry technology transfer office should re-establish again as University-Industry Linkage office with a directorate level. Keywords: Academicians, Industry, Linkage, knowledge transfer, University

Marketing of Banking Service and Its Impact on the Profitability of Ethiopian Private Commercial Banks

Marketing and advertising is a fundamental concept in the banking industry and profit also the key point which helps them to be surviving in the market. Therefore, this study aims to investigate the marketing of banking service and its impact on the profitability of Ethiopian private commercial banks. The sample of the study included only private commercial banks operating in the country during the study period. To achieve the purposes of the study, and to analyze the data extracted from the annual reports during 2011 to 2017, the researcher used multiple linear regression method. For this purpose the collected data were analyzed using the STATA14 software. The result showed that positive and significant effect of commission income and number of branches on the profitability of the banks. Whereas there is no significant effect of deposit ratio and advertising expense on the profitability of the bank. Keywords: Marketing mix, profitability, advertising expense, banking service DOI: 10.7176/EJBM/11-1-0