Constrained Representations of Map Graphs and Half-Squares

The square of a graph H, denoted H^2, is obtained from H by adding new edges between two distinct vertices whenever their distance in H is two. The half-squares of a bipartite graph B=(X,Y,E_B) are the subgraphs of B^2 induced by the color classes X and Y, B^2[X] and B^2[Y]. For a given graph G=(V,E_G), if G=B^2[V] for some bipartite graph B=(V,W,E_B), then B is a representation of G and W is the set of points in B. If in addition B is planar, then G is also called a map graph and B is a witness of G [Chen, Grigni, Papadimitriou. Map graphs. J. ACM49 (2) (2002) 127-138]. While Chen, Grigni, Papadimitriou proved that any map graph G=(V,E_G) has a witness with at most 3|V|-6 points, we show that, given a map graph G and an integer k, deciding if G admits a witness with at most k points is NP-complete. As a by-product, we obtain NP-completeness of edge clique partition on planar graphs; until this present paper, the complexity status of edge clique partition for planar graphs was previously unknown. We also consider half-squares of tree-convex bipartite graphs and prove the following complexity dichotomy: Given a graph G=(V,E_G) and an integer k, deciding if G=B^2[V] for some tree-convex bipartite graph B=(V,W,E_B) with |W|<=k points is NP-complete if G is non-chordal dually chordal and solvable in linear time otherwise. Our proof relies on a characterization of half-squares of tree-convex bipartite graphs, saying that these are precisely the chordal and dually chordal graphs

Complexity results for matching cut problems in graphs without long induced paths

In a graph, a (perfect) matching cut is an edge cut that is a (perfect) matching. Matching Cut (MC), respectively, Perfect Matching Cut (PMC), is the problem of deciding whether a given graph has a matching cut, respectively, a perfect matching cut. The Disconnected Perfect Matching problem (DPM) is to decide if a graph has a perfect matching that contains a matching cut. Solving an open problem recently posed in [Lucke, Paulusma, Ries (ISAAC 2022), and Feghali, Lucke, Paulusma, Ries (arXiv:2212.12317)], we show that PMC is NP-complete in graphs without induced 14-vertex path $P_{14}$. Our reduction also works simultaneously for MC and DPM, improving the previous hardness results of MC on $P_{19}$-free graphs and of DPM on $P_{23}$-free graphs to $P_{14}$-free graphs for both problems. Actually, we prove a slightly stronger result: within $P_{14}$-free graphs, it is hard to distinguish between (i) those without matching cuts and those in which every matching cut is a perfect matching cut, (ii) those without perfect matching cuts and those in which every matching cut is a perfect matching cut, and (iii) those without disconnected perfect matchings and those in which every matching cut is a perfect matching cut. Moreover, assuming the Exponential Time Hypothesis, none of these problems can be solved in time $2^{o(n)}$ for $n$-vertex $P_{14}$-free input graphs. We also consider the problems in graphs without long induced cycles. It is known that MC is polynomially solvable in graphs without induced cycles of length at least 5 [Moshi (JGT 1989)]. We point out that the same holds for DPM.Comment: To appear in the proceedings of WG 202

Air Emission Inventory

Emission inventory (EI) is a comprehensive listing of pollutants from all sources in a geo-graphical area during a period of time. The development of EI database is very important to air quality management and helps us to find out main sources. In general, to develop a reliable EI for one specific area, the following steps are involved: (i) list the types of sources, (ii) determine the types of air pollutant emission from each of the listed sources, (iii) find out the emission factor (EF) for each of the concerned pollutants, (iv) determine the number and size of specific sources in the area, and (v) multiply the appropriate numbers from step (iii) and (iv) to obtain the total emissions and then sum up the similar emissions to obtain the total for the area. With emission inventory, we can define the main sources in the study area and have the best solution for clean air action. Besides, the result from EIs can be used to study in other sectors related to human health, economic loss from air pollution, etc. This chapter will describe the method for development of an air emission inventory for developing and developed countries

Operation and results of a vegetable market information and consultation system in Vietnam

This report presents the operation and results of a vegetable market information and consultation system (MICS), set up between 2002 and 2005 in Hanoi, to address marketing problems faced by vegetable farmers. A MICS is a market information system (MIS) combined with debates organised among farmers, traders, and development agents to reach common visions and strategies on marketing. Information collected in the first years relating to indicators of origin and supply deficits was disseminated to farmers and extension agents through newsletters and consultation meetings. The process then focused on making daily prices available, as requested by the farmers. The system was based on a network of contact traders and dissemination was by television. The workshops made it possible to reach a consensus for market opportunities arising from periods of supply deficit for some vegetables and how to take advantage of this situation, especially for tomatoes and cabbage imported from China during the rainy season, which presented some quality differences compared to the local products. With regards to price information, the majority of farmers and traders, surveyed by a quick-impact appraisal, stated they had access through television on a regular basis and that they used price information mostly to bargain with traders. Back up for a permanent ''safe'' vegetable producer and trader association was one of the outputs of the MICS. Our experience shows that price dissemination was easier to sustain (with the involvement of the public sector) than the consultation workshops, generally due to low local capacity in terms of meeting facilitation and the present weakness of extension services and sector organisations. (Résumé d'auteur