Alpha-Degree Closures for Graphs

Bondy and Chvatal [7] introduced a general and unified approach to a variety of graph-theoretic problems. They defined the k-closure Ck(G), where k is a positive integer, of a graph G of order n as the graph obtained from G by recursively joining pairs of nonadjacent vertices a,b satisfying the condition C(a,b): d(a) + d(b) >= k. From many properties P, they found a suitable k (depending on P and n) such that Ck(G) has property P if and only if G does. For instance, if P is the hamiltonian property, then k=n. In [3], we proved that C(a,b) can be replaced by d(a) + d(b) + |Q(G)| >= k, where Q(G) is a well-defined subset of vertices nonadjacent to a,b. In [4], we proved that, for a (2+k-n)-connected graph, C(a,b) can be replaced by |N(a) U N(b)| + d_ab + e_ab >= k, where e_ab is a well-defined binary variable and d_ab is the minimum degree over all vertices distinct from a,b and non adjacent to them. The condition on connectivity is a necessary one. In this paper, we show that C(a,b) can be replaced by the condition d(a) + d(b) (â_ab - a_ab) >= k, where â_ab and a_ab are respectively the order and independence number of the subgraph G - N(a) U N(b).closure, degree closure, neighborhood closure, dual closure, stability, hamiltonicity, cyclability, degree sequence, matching number, k-leaf-connected

Temperature evolution of domains and intradomain chirality in 1T- TaS2

We use scanning tunneling microscopy to study the temperature evolution of the atomic-scale properties of the nearly commensurate charge density wave (NC-CDW) state of the low-dimensional material 1T-TaS2. Our measurements at 203, 300, and 354 K, roughly spanning the temperature range of the NC-CDW state, show that while the average CDW periodicity is temperature independent, domaining and the local evolution of the CDW lattice within a domain are temperature dependent. Further, we characterize the temperature evolution of the displacement field associated with the recently discovered intradomain chirality of the NC-CDW state by calculating the local rotation vector. Intradomain chirality throughout the NC-CDW phase is likely driven by a strong coupling of the CDW lattice to the atomic lattice. © 2023 American Physical Society

cpDNA supports the identification of the major lineages of American <i>Blechnum</i> (Blechnaceae, Polypodiopsida) established by morphology

Blechnaceae is an important leptosporangiate family (9–10 genera, about 250 species). It is monophyletic and distributed mainly in tropical America and Australasia. Among the species 80% belong to Blechnum, a genus with a very complex taxonomy and uncertain internal relationships. In terms of American diversity, the results of morphological studies have arrived at 8 informal groups. Molecular works on this genus are scarce, and there is no information for the majority of American species. The main objective of this work was to evaluate whether the groups proposed to organise the diversity of American of Blechnum are consistent with a molecular analysis. We sequenced 2 chloroplastic regions from species representing all of the groups. In our molecular analysis most of the informal groups were maintained as well supported clades. Only 2 species, B. brasiliense and B. spicant, appear to be isolated from their alleged relatives. Combining our molecular results with previous morphological knowledge, we propose the recognition of 4 lineages: 1) B. serrulatum , 2) B. spicant, and 3) core Blechnum, which represents a large clade that can be divided into core Blechnum I (arborescent species, cordatoids, and B. brasiliense) and core Blechnum II (epiphytic species and herbaceous terrestrials, both monomorphic and dimorphic groups).Facultad de Ciencias Naturales y Muse

A tale of two Spartinas: Climatic, photobiological and isotopic insights on the fitness of non-indigenous versus native species

International audienceSalt marshes are facing a new threat: the invasion by non-indigenous species (NIS), Although its introduction time is not established yet, in 1999 Spartina versicolor was already identified as a NIS in the Mediterranean marshes, significantly spreading its area of colonization. Using the Mediterranean native Spartina maritima as a reference, the present research studied the ecophysiological fitness of this NIS in its new environment, as a tool to understand its potential invasiveness. It was found that Spartina versicolor had a stable photobiological pattern, with only minor fluctuations during an annual cycle, and lower efficiencies comparated to S. maritima. The NIS seems to be rather insensitive to the observed abiotic factors fluctuations (salinity and pH of the sediment), and thus contrasts with the native S. maritima, known to be salinity dependent with higher productivity values in higher salinity environments. Most of the differences observed between the photobiology of these species could be explained by their nitrogen nutrition (here evaluated by the δ15N stable isotope) and directly related with the Mediterranean climate. Enhanced by a higher N availability during winter, the primary production of S. maritima which lead to dilution of the foliar δ15N concentration in the newly formed biomass, similarly to what is observed along a rainfall gradient. On the other hand, S. versicolor showed an increased δ15N in its tissues along the annual rainfall gradient, probably due to a δ15N concentration effect during low biomass production periods (winter and autumn). Together with the photobiological traits, these isotopic data point out to a climatic misfit of S. versicolor to the Mediterranean climate compared to the native S. maritima. This appears to be the major constrain shaping the ecophysiological fitness of this NIS, its primary production and consequently, its spreading rate along the Mediterranean marshes

Characterization of duplicate gene evolution in the recent natural allopolyploid Tragopogon miscellus by next-generation sequencing and Sequenom iPLEX MassARRAY genotyping

The definitive version is available at www.blackwell-synergy.co

cpDNA supports the identification of the major lineages of American <i>Blechnum</i> (Blechnaceae, Polypodiopsida) established by morphology

Blechnaceae is an important leptosporangiate family (9–10 genera, about 250 species). It is monophyletic and distributed mainly in tropical America and Australasia. Among the species 80% belong to Blechnum, a genus with a very complex taxonomy and uncertain internal relationships. In terms of American diversity, the results of morphological studies have arrived at 8 informal groups. Molecular works on this genus are scarce, and there is no information for the majority of American species. The main objective of this work was to evaluate whether the groups proposed to organise the diversity of American of Blechnum are consistent with a molecular analysis. We sequenced 2 chloroplastic regions from species representing all of the groups. In our molecular analysis most of the informal groups were maintained as well supported clades. Only 2 species, B. brasiliense and B. spicant, appear to be isolated from their alleged relatives. Combining our molecular results with previous morphological knowledge, we propose the recognition of 4 lineages: 1) B. serrulatum , 2) B. spicant, and 3) core Blechnum, which represents a large clade that can be divided into core Blechnum I (arborescent species, cordatoids, and B. brasiliense) and core Blechnum II (epiphytic species and herbaceous terrestrials, both monomorphic and dimorphic groups).Laboratorio de Estudios de Anatomía Vegetal Evolutiva y Sistemátic

Multiple Origins and Nested Cycles of Hybridization Result in High Tetraploid Diversity in the Monocot Prospero

This work was supported by the Austrian Science Fund (FWF P21440-B03 to HW-S)

Hybridization and hybrid speciation under global change

An unintended consequence of global change is an increase in opportunities for hybridization among previously isolated lineages. Here we illustrate how global change can facilitate the breakdown of reproductive barriers and the formation of hybrids, drawing on the flora of the British Isles for insight. Although global change may ameliorate some of the barriers preventing hybrid establishment, for example by providing new ecological niches for hybrids, it will have limited effects on environment-independent post-zygotic barriers. For example, genic incompatibilities and differences in chromosome numbers and structure within hybrid genomes are unlikely to be affected by global change. We thus speculate that global change will have a larger effect on eroding pre-zygotic barriers (eco-geographical isolation and phenology) than post-zygotic barriers, shifting the relative importance of these two classes of reproductive barriers from what is usually seen in naturally produced hybrids where pre-zygotic barriers are the largest contributors to reproductive isolation. Although the long-term fate of neo-hybrids is still to be determined, the massive impact of global change on the dynamics and distribution of biodiversity generates an unprecedented opportunity to study large numbers of unpredicted, and often replicated, hybridization ‘experiments’, allowing us to peer into the birth and death of evolutionary lineages