Narrow Results

Let $F$, $G$ and $H$ be three graphs. We write $F\to (G,H)$ if any red-blue edge-colored $F$ contains either a red subgraph $G$ or a blue subgraph $H$. The size Ramsey number $\mathrm{\text{r̂}}(G,H)$ of two graphs $G$ and $H$, introduced by Erdős et al., is defined as $\mathrm{\text{r̂}}(G,H)=min\{|E(F)|:F\to (G,H)\}$. In this paper, we obtain some upper and lower bounds and some exact values of $\mathrm{\text{r̂}}(G,H)$, where $G\in \{2P_2,P_3\}$ and $H$ are some brooms.

We prove #P-completeness for counting the number of forests in regular graphs and chordal graphs. We also present algorithms for this problem, running in O*(1.8494^m) time for 3-regular graphs, and O*(1.9706^m) time for unit interval graphs, where m is the number of edges in the graph and O*-notation ignores a polynomial factor. The algorithms can be generalized to the Tutte polynomial computation.

Submultiplicativity, an analytic property generalizing the Strengthened Hanna Neumann Conjecture (SHNC) to complexes was proved in [2] assuming the deep-fall property. This in particular implied SHNC. The purpose of this note is to write the proof of the original SHNC and purely in terms of groups and graphs. We also give explicit examples showing that the upper bound in SHNC is sharp.

Forests are widely believed to provide a water purification service that reduces the cost of treating drinking water, but few empirical economic studies have investigated this service in developing countries, where deforestation rates and thus threats to the service tend to be higher than in developed countries. Even fewer studies have investigated the distribution of the benefits of this service, or any other regulating ecosystem service for that matter, in either developing or developed countries. Using quarterly panel data for 158 water utilities in Thailand during 2004–2014, we find robust evidence that forests significantly reduced the material cost of water treatment, but we find no evidence that the cost reductions were progressive in the sense of being larger in provinces with higher poverty rates. The economic justification for source water protection in Thailand appears to hinge purely on considerations of efficiency — does source water protection provide net benefits? — not on the distribution of those benefits between poorer and richer locations. Research in other countries is needed to determine if the absence of pro-poor distributional impacts of forest water purification is unique to Thailand or the norm and if interventions that enhance forest water purification significantly reduce poverty in locations served by treated drinking water systems.

This research examines the carbon capture potential and timber production outcomes of conventional logging (CVL) and reduced impact logging (RIL) in the Mekong region of Southeast Asia from 1990 to 2050, showing that CVL resulted in approximately 4590.9 TgCO₂ in carbon emissions during the study period, while RIL demonstrated a notable annual reduction of 10.9 TgCO₂ in carbon emissions, alongside sustainable annual production of 11.4 million m3 of wood. Plantation forests (PF) contributed to an annual carbon removal of 58.69 TgCO₂ over the course of the study. Implementing forest management practices in the Mekong may also generate significant carbon revenues, estimated at USD 3,500.07 million within the Paris Agreement period 2020–2030, contingent upon prevailing carbon pricing mechanisms. Embracing sustainable forest management (SFM) and restoration strategies, with emphasis on RIL, may drive improvements in quality of wood products, waste reduction, and natural carbon capture enhancement.

We compared soil microbial communities of forests infected with Heterobasidion parviporum and Armillaria spp. with soils of healthy forests using conventional plating and molecular methods. Plate counts from the soils of the infected forests reflected a significant decrease of the number of cultivable filamentous fungi (CFF) and a slight decrease of the total number of cultivable microorganisms. The diversity of CFF was reduced in the stands infected with H. parviporum. In the stands infected with Armillaria spp. the diversity of CFF and relative abundance of cultivable Trichoderma spp. was even higher than in healthy forest stands. Quantitative PCR revealed increased concentrations of total fungal DNA and Trichoderma spp. DNA in the soil of H. parviporum infected stands. In Armillaria spp. infected stands the total concentration of fungal DNA was decreased, but relative amount of Trichoderma spp. DNA was increased. No significant differences in the species diversity of fungi in the soil were found by ARDRA.

Given finite simple graph one can associate the edge ideal. In this paper we discuss the non-vanishingness of the graded Betti numbers of edge ideals in terms of the original graph. In particular, we give a necessary and sufficient condition for a chordal graph on which the graded Betti number does not vanish and characterize the graded Betti number for a forest. Moreover we characterize the projective dimension for a chordal graph.

Forests are essential for survival and sustenance of life. Their growth should be optimized so that greater benefits are derived from them. With such a large establishment and geographical base, the monitoring and decision making becomes very critical. The inherent delays hamper the decision process required at a particular time. The increasing area covered by forest plantations creates a demand for trustworthy mechanisms to ensure they are responsibly established and managed. However, most are focused exclusively or prevalently on natural or semi-natural forests, while only a few are specific to planted forests or plantations. The main aim is to assess whether and to what extent planted forests are properly considered within the existing sets of standards/guidelines and to identify areas for improvements, is based on a series of comparative analysis. This paper focus to carry out the full potential of convergence of GIS and Mobile Technology for plantation, with emphasis on technically viable infrastructure solution based on sustainability principles. Integration of GIS and Mobile is being proposed with an objective to enable a single window access to information and services being provided by various formations and to establish a collaborated environment.