Very well covered graphs

AbstractA graph is well-covered if it has no isolated vertices and all the maximal stable (independent) sets have the same cardinality. If furthermore this cardinality is equal to 12n, where n is the order of the graph, the graph is called ‘very well covered’. The class of very well-covered graphs contains in particular the bipartite well-covered graphs studied by Ravindra. In this article, we characterize the very well covered-graphs and give some of their properties

Changing upper irredundance by edge addition

AbstractDenote the upper irredundance number of a graph G by IR(G). A graph G is IR-edge-addition-sensitive if its upper irredundance number changes whenever an edge of Ḡ is added to G. Specifically, G is IR-edge-critical (IR+-edge-critical, respectively) if IR(G+e)<IR(G) (IR(G+e)>IR(G), respectively) for each edge e of Ḡ. We show that if G is IR-edge-addition-sensitive, then G is either IR-edge-critical or IR+-edge-critical. We obtain properties of the latter class of graphs, particularly in the case where β(G)=IR(G)=2 (where β(G) denotes the vertex independence number of G). This leads to an infinite class of IR+-edge-critical graphs where IR(G)=2

The trophoblast giant cells of cricetid rodents

Giant cells are a prominent feature of placentation in cricetid rodents. Once thought to be maternal in origin, they are now known to be trophoblast giant cells (TGCs). The large size of cricetid TGCs and their nuclei reflects a high degree of polyploidy. While some TGCs are found at fixed locations, others migrate throughout the placenta and deep into the uterus where they sometimes survive postpartum. Herein, we review the distribution of TGCs in the placenta of cricetids, including our own data from the New World subfamily Sigmodontinae, and attempt a comparison between the TGCs of cricetid and murid rodents. In both families, parietal TGCs are found in the parietal yolk sac and as a layer between the junctional zone and decidua. In cricetids alone, large numbers of TGCs, likely from the same lineage, accumulate at the edge of the placental disk. Common to murids and cricetids is a haemotrichorial placental barrier where the maternal-facing layer consists of cytotrophoblasts characterized as sinusoidal TGCs. The maternal channels of the labyrinth are supplied by trophoblast-lined canals. Whereas in the mouse these are lined largely by canal TGCs, in cricetids canal TGCs are interspersed with syncytiotrophoblast. Transformation of the uterine spiral arteries occurs in both murids and cricetids and spiral artery TGCs line segments of the arteries that have lost their endothelium and smooth muscle. Since polyploidization of TGCs can amplify selective genomic regions required for specific functions, we argue that the TGCs of cricetids deserve further study and suggest avenues for future research

Chorioallantoic placentation in Galea spixii (Rodentia, Caviomorpha, Caviidae)

<p>Abstract</p> <p>Background</p> <p>Placentas of guinea pig-related rodents are appropriate animal models for human placentation because of their striking similarities to those of humans. To optimize the pool of potential models in this context, it is essential to identify the occurrence of characters in close relatives.</p> <p>Methods</p> <p>In this study we first analyzed chorioallantoic placentation in the prea, Galea spixii, as one of the guinea pig's closest relatives. Material was collected from a breeding group at the University of Mossoró, Brazil, including 18 individuals covering an ontogenetic sequence from initial pregnancy to term. Placentas were investigated by means of histology, electron microscopy, immunohistochemistry (vimentin, α-smooth muscle actin, cytokeration) and proliferation activity (PCNA).</p> <p>Results</p> <p>Placentation in Galea is primarily characterized by an apparent regionalization into labyrinth, trophospongium and subplacenta. It also has associated growing processes with clusters of proliferating trophoblast cells at the placental margin, internally directed projections and a second centre of proliferation in the labyrinth. Finally, the subplacenta, which is temporarily supplied in parallel by the maternal and fetal blood systems, served as the center of origin for trophoblast invasion.</p> <p>Conclusion</p> <p>Placentation in Galea reveals major parallels to the guinea pig and other caviomorphs with respect to the regionalization of the placenta, the associated growing processes, as well as trophoblast invasion. A principal difference compared to the guinea pig occurred in the blood supply of the subplacenta. Characteristics of the invasion and expanding processes indicate that Galea may serve as an additional animal model that is much smaller than the guinea pig and where the subplacenta partly has access to both maternal and fetal blood systems.</p

Placentation in Sigmodontinae: a rodent taxon native to South America

Background: Sigmodontinae, known as ""New World rats and mice,"" is a large subfamily of Cricetidae for which we herein provide the first comprehensive investigation of the placenta. Methods: Placentas of various gestational ages ranging from early pregnancy to near term were obtained for five genera, i.e. Necromys, Euryoryzomys, Cerradomys, Hylaeamys, and Oligoryzomys. They were investigated by means of histology, immunohistochemistry, a proliferation marker, DBA-lectin staining and transmission electron microscopy. Results: The chorioallantoic placenta was organized in a labyrinthine zone, spongy zone and decidua and an inverted yolk sac persisted until term. The chorioallantoic placenta was hemotrichorial. The interhemal barrier comprised fetal capillary endothelium and three layers of trophoblast, an outermost, cellular layer and two syncytial ones, with interspersed trophoblast giant cells (TGC). In addition, accumulations of TGC occurred below Reichert's membrane. The junctional zone contained syncytial trophoblast, proliferative cellular trophoblast, glycogen cells and TGC that were situated near to the maternal blood channels. In three of the genera, TGC were also accumulated in distinct areas at the placental periphery. PAS-positive glycogen cells derived from the junctional zone invaded the decidua. Abundant maternal uNK cells with positive response to PAS, vimentin and DBA-lectin were found in the decidua. The visceral yolk sac was completely inverted and villous. Conclusion: The general aspect of the fetal membranes in Sigmodontinae resembled that found in other cricetid rodents. Compared to murid rodents there were larger numbers of giant cells and in some genera these were seen to congregate at the periphery of the placental disk. Glycogen cells were found to invade the decidua but we did not identify trophoblast in the walls of the deeper decidual arteries. In contrast these vessels were surrounded by large numbers of uNK cells. This survey of wild-trapped specimens from five genera is a useful starting point for the study of placentation in an important subfamily of South American rodents. We note, however, that some of these rodents can be captive bred and recommend that future studies focus on the study of time dated pregnancies.This research was supported by grants from FAPESP (Proc. 07/51491-3 and\ud 09/53392-8)

Chorioallantoic and yolk sac placentation in the plains viscacha (Lagostomus maximus) - A caviomorph rodent with natural polyovulation

Objectives: Reproduction in the plains viscacha is characterized by the polyovulation of hundreds of oocytes, the loss of implantation and the development of 1-3 offspring. Our goal was to determine whether placental development was affected by these specializations. Study design: Thirteen placentas from early pregnancy to near-term pregnancy were analyzed using histological, immunohistochemical and transmission electron microscopy. Results: An inverted, villous yolk sac was present. Placentas were formed by the trophospongium, labyrinth and subplacenta. A lobulated structure with a hemomonochorial barrier was established early in pregnancy. Proliferating trophoblast that was clustered at the outer border and inside the labyrinth was responsible for placental growth. Trophoblast invasion resulted from the cellular trophoblast and syncytial streamers derived from the subplacenta. Different from other caviomorphs, numerous giant cells were observed. Conclusions: The principle processes of placentation in caviomorphs follow an extraordinarily stable pattern that is independent of specializations, such as polyovulation.Facultad de Ciencias Veterinaria

Placentation and fetal membrane development in the South American coati, Nasua nasua (Mammalia, Carnivora, Procyonidae)

Abstract\ud \ud Background\ud Placental research in carnivores has concentrated on domestic species, which have zonary, labyrinthine placentas with an endotheliochorial barrier. Although the coati, Nasua nasua, is a widely distributed species in South America, data on the development of the placenta and the fetal membranes in this species are very sparse.\ud \ud \ud Findings\ud Four placentas from mid-gestation to near term were collected from wild individuals and were investigated based on gross morphology, histology, immunohistochemistry and electron microscopy. The available data support the concept that the ancestral condition of placentation in carnivores is phylogenetically characterized by a zonary and labyrinthine placental type with an endotheliochorial fetomaternal barrier, comprising extended epitheliochorial and haemochorial zones, such as hemophagous organs for iron supply and histiotrophe uptake and a yolk sac placenta.\ud \ud \ud Conclusions\ud Because of the foundational mechanisms that lead to the considerable complexity of fetomaternal contact zones in carnivores have not been studied, carnivores are interesting animal models for interhaemal barrier differentiation.Financial support was provided by FAPESP (2009/51606-0)

Morphometric analysis of the placenta in the New World mouse Necromys lasiurus (Rodentia, Cricetidae): a comparison of placental development in cricetids and murids

Background: Stereology is an established method to extrapolate three-dimensional quantities from two-dimensional images. It was applied to placentation in the mouse, but not yet for other rodents. Herein, we provide the first study on quantitative placental development in a sigmodontine rodent species with relatively similar gestational time. Placental structure was also compared to the mouse, in order to evaluate similarities and differences in developmental patterns at the end of gestation. Methods: Fetal and placental tissues of Necromys lasiurus were collected and weighed at 3 different stages of gestation (early, mid and late gestation) for placental stereology. The total and relative volumes of placenta and of its main layers were investigated. Volume fractions of labyrinth components were quantified by the One Stop method in 31 placentae collected from different individuals, using the Mercator® software. Data generated at the end of gestation from N. lasiurus placentae were compared to those of Mus musculus domesticus obtained at the same stage. Results: A significant increase in the total absolute volumes of the placenta and its main layers occurred from early to mid-gestation, followed by a reduction near term, with the labyrinth layer becoming the most prominent area. Moreover, at the end of gestation, the total volume of the mouse placenta was significantly increased compared to that of N. lasiurus although the proportions of the labyrinth layer and junctional zones were similar. Analysis of the volume fractions of the components in the labyrinth indicated a significant increase in fetal vessels and sinusoidal giant cells, a decrease in labyrinthine trophoblast whereas the proportion of maternal blood space remained stable in the course of gestation. On the other hand, in the mouse, volume fractions of fetal vessels and sinusoidal giant cells decreased whereas the volume fraction of labyrinthine trophoblast increased compared to N. lasiurus placenta. Conclusions: Placental development differed between N. lasiurus and M. musculus domesticus. In particular, the low placental efficiency in N. lasiurus seemed to induce morphological optimization of fetomaternal exchanges. In conclusion, despite similar structural aspects of placentation in these species, the quantitative dynamics showed important differences.For technical support we thank Marie-Christine Aubrière, Michèle Dahirel of the Institut National de la Recherche Agronomique, Jouy-en-Josas, as well as members of the Universidade Federal Rural do Semi-Árido, Mossoró. We thank also Yves Maurin for Nanozoomer facilities. This research was supported by INRA and by grants from FAPESP (Process number: 09/53392-8).INRAFAPESP [09/53392-8

TOPOGRAFIA E MORFOLOGIA DAS VÍSCERAS DO PERIQUITO-AUSTRALIANO (Melopsittacus undulatus, SHAW 1805)

Em virtude da escassez de dados referentes à morfologia e topografia das aves em geral, o presente estudo teve como objetivo descrever a topografia e morfologia das vísceras do periquito-australiano (Melopsittacus undulatus), para assim proporcionar um conhecimento mais amplo sobre características específicas dessa espécie. Para a descrição da morfologia e topografia das vísceras foram utilizados dez periquitos, sendo cinco machos e cinco fêmeas. Os animais foram fixados com solução de formaldeído 10%, através de perfusão na musculatura e cavidade visceral. Macroscopicamente, as vísceras do periquito não apresentaram muitas diferenças comparadas a outras espécies de aves domésticas. Microscopicamente, a principal diferença estava na presença de mecanorreceptores (corpúsculos de Pacini) na língua, encontrados pela primeira vez nesta espécie de psitaciforme.  PALAVRAS-CHAVES: Melopsittacus undulatus, morfologia, topografia, vísceras

On the (parameterized) complexity of recognizing well-covered (r,l)-graphs.

An (r,ℓ)(r,ℓ)-partition of a graph G is a partition of its vertex set into r independent sets and ℓℓ cliques. A graph is (r,ℓ)(r,ℓ) if it admits an (r,ℓ)(r,ℓ)-partition. A graph is well-covered if every maximal independent set is also maximum. A graph is (r,ℓ)(r,ℓ)-well-covered if it is both (r,ℓ)(r,ℓ) and well-covered. In this paper we consider two different decision problems. In the (r,ℓ)(r,ℓ)-Well-Covered Graph problem ((r,ℓ)(r,ℓ) wcg for short), we are given a graph G, and the question is whether G is an (r,ℓ)(r,ℓ)-well-covered graph. In the Well-Covered (r,ℓ)(r,ℓ)-Graph problem (wc (r,ℓ)(r,ℓ) g for short), we are given an (r,ℓ)(r,ℓ)-graph G together with an (r,ℓ)(r,ℓ)-partition of V(G) into r independent sets and ℓℓ cliques, and the question is whether G is well-covered. We classify most of these problems into P, coNP-complete, NP-complete, NP-hard, or coNP-hard. Only the cases wc(r, 0)g for r≥3r≥3 remain open. In addition, we consider the parameterized complexity of these problems for several choices of parameters, such as the size αα of a maximum independent set of the input graph, its neighborhood diversity, or the number ℓℓ of cliques in an (r,ℓ)(r,ℓ)-partition. In particular, we show that the parameterized problem of deciding whether a general graph is well-covered parameterized by αα can be reduced to the wc (0,ℓ)(0,ℓ) g problem parameterized by ℓℓ, and we prove that this latter problem is in XP but does not admit polynomial kernels unless coNP⊆NP/polycoNP⊆NP/poly