Complements of nearly perfect graphs

A class of graphs closed under taking induced subgraphs is $\chi$-bounded if there exists a function $f$ such that for all graphs $G$ in the class, $\chi(G) \leq f(\omega(G))$. We consider the following question initially studied in [A. Gy{\'a}rf{\'a}s, Problems from the world surrounding perfect graphs, {\em Zastowania Matematyki Applicationes Mathematicae}, 19:413--441, 1987]. For a $\chi$-bounded class $\cal C$, is the class $\bar{C}$ $\chi$-bounded (where $\bar{\cal C}$ is the class of graphs formed by the complements of graphs from $\cal C$)? We show that if $\cal C$ is $\chi$-bounded by the constant function $f(x)=3$, then $\bar{\cal C}$ is $\chi$-bounded by $g(x)=\lfloor\frac{8}{5}x\rfloor$ and this is best possible. We show that for every constant $c>0$, if $\cal C$ is $\chi$-bounded by a function $f$ such that $f(x)=x$ for $x \geq c$, then $\bar{\cal C}$ is $\chi$-bounded. For every $j$, we construct a class of graphs $\chi$-bounded by $f(x)=x+x/\log^j(x)$ whose complement is not $\chi$-bounded

Vertices with the Second Neighborhood Property in Eulerian Digraphs

The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property. A cycle intersection graph of an even graph is a new graph whose vertices are the cycles in a cycle decomposition of the original graph and whose edges represent vertex intersections of the cycles. By using a digraph variant of this concept, we prove that Eulerian digraphs which admit a simple dicycle intersection graph have not only adhere to the Second Neighborhood Conjecture, but have a vertex of minimum outdegree that has the Second Neighborhood Property.Comment: fixed an error in an earlier version and made structural change

Vertices with the Second Neighborhood Property in Eulerian Digraphs

The Second Neighborhood Conjecture states that every simple digraph has a vertex whose second out-neighborhood is at least as large as its first out-neighborhood, i.e. a vertex with the Second Neighborhood Property. A cycle intersection graph of an even graph is a new graph whose vertices are the cycles in a cycle decomposition of the original graph and whose edges represent vertex intersections of the cycles. By using a digraph variant of this concept, we prove that Eulerian digraphs which admit a simple cycle intersection graph have not only adhere to the Second Neighborhood Conjecture, but that local simplicity can, in some cases, also imply the existence of a Seymour vertex in the original digraph.Comment: This is the version accepted for publication in Opuscula Mathematic

Response of Tomato (Lycopersicon esculentum): Growth and Yield, to Rates of Mineral and Poultry Manure Application in the Guinea Savanna Agro-ecological Zone in Nigeria

The study was designed to evaluate the impact of different levels of poultry manures (PM) on the growth and yield of tomato in comparison to mineral fertilizer (MF) and the combine treatment of PM + MF. The combined analysis revealed that application of poultry manure at 150 kg N/ha gave the tallest plant height, but not significantly different from application of manure at 300 kg N/ha. These were however, significantly different from the inorganic fertilizer treatment; an indication that tomato responded better to poultry manure than mineral fertilizer, in respect of plant height. Application of inorganic fertilizer at the rate of 300 kg N/ha gave significantly taller crop than 150 kg N/ha. The shortest plant heights were observed in the control treatment in both cropping seasons as well as in the combined result. Application of organic and inorganic fertilizers significantly (p ≤ 0.05) influenced total number of harvested tomato and weight of harvest. Application of 150 kg PM/ha + 150 kg MF/ha gave the best yield, which was significantly different from other rates investigated, followed by 75 kg PM/ha + 75 kg MF/ha. While increasing poultry manure rate from 150 kg N/ha to 300 kg N/ha led to an increase in total number of harvested tomato and tomato yield / ha, increasing mineral fertilizer rate from 150 kg N/ha to 300 kg N/ha actually depressed tomato yield and number of tomato harvested per plot. Finally, application of inorganic nutrient at the rate of 150 kg N/ha yielded 88.15% return over the control, while applying 300 kg N/ha inorganic nutrient yielded only 74.68% return over the control. Application of organic nutrient at the rate of 150 and 300 kg N/ha yielded 81.93 and 85.98 percent returns, respectively over the control treatment. The highest return, however, was obtained with the application of 150 kg PM/ha + 150 kg MF/ha (90.17%) over the control, which was followed by application of 75 kg PM/ha + 75 kg MF/ha (89.42%) over the control. Based on the research outcome, it is recommended that if tomato is to be grown on inorganic fertilizer, application of N at the rate of 150 kg/ha is appropriate, while application of organic fertilizer at the rate of 300 kg N/ha is recommended. However, combine application of 150 kg PM/ha + 150 kg MF/ha is recommended for optimum tomato yield. Keywords: Height, plant gilt, growth, development, yield and economic

Acquisition of Hindi's laryngeal contrast by Meiteilon speakers

Though Meeteilon does not have phonemic contrast in voicing, native speakers can accurately recognize voiced stops and aspirated voiced stops in word initial positions and categorically distinguish these from voiceless stops and aspirated voiceless stops. However, they are unable to perceive any of these laryngeal contrasts in word-final position. We explain these facts by proposing that tone and aspiration being phonemic in Meeteilon, these cues from L1 can be re-recruited by native speakers for learning laryngeal contrasts in a second language like Hindi. Since these cues from L1 cannot be used to perceive laryngeal contrasts in word-final position, the contrasts are not perceived in these positions

Enhancing naming and location services to support multi-homed devices in heterogeneous environments

The growth of the Mobile Internet is being fuelled by the development of heterogeneous devices which have several wireless interfaces. This brings new challenges which require a critical examination of current Internet Infrastructure with a view to providing better support for mobility, multi-homing and virtual networking. This paper considers a recently published solution to the multi-homing issue, and based on that proposes enhancements to support the core location and naming servers with the introduction of the Master Locator and the Enhanced DNS