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Summer fire in steppe habitats: long-term effects on vegetation and autumnal assemblages of cursorial arthropods

Abstract

Being an essential driving factor in dry grassland ecosystems, uncontrolled fires can cause damage to isolated natural areas. We investigated a case of a small-scale mid-summer fire in an abandoned steppe pasture in northeastern Ukraine and focused on the post-fire recovery of arthropod assemblages (mainly spiders and beetles) and vegetation pattern. The living cover of vascular plants recovered in a year, while the cover of mosses and litter remained sparse for four years. The burnt site was colonised by mobile arthropods occurring in surrounding grasslands. The fire had no significant impact on arthropod diversity or abundance, but changed their assemblage structure, namely dominant complexes and trophic guild ratio. The proportion of phytophages reduced, while that of omnivores increased. The fire destroyed the variety of the arthropod assemblages created by the patchiness of vegetation cover. In the post-fire stage they were more similar to each other than at the burnt plot in the pre- and post-fire period. Spider assemblages tended to recover their pre-fire state, while beetle assemblages retained significant differences during the entire study period.

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The tribe Scrophularieae (Scrophulariaceae): A Review of Phylogenetic Studies

Abstract

Molecular data have been increasingly used to study the phylogenetic relationships among many taxa, including scrophs. Sometimes they have provided phylogenetic reconstructions that are in conflict with morphological data leading to a re-evaluation of long-standing evolutionary hypotheses. In this paper, we review reports of the recent knowledge of the phylogenetic relationships within Scrophularieae (2011–2017). The results of these analyses led to the following conclusions. (1) Species of Scrophularia have undergone one or more Miocene migration events occurred from eastern Asia to the North America with subsequent long dispersal and diversification in three main directions. (2) Allopolyploid and aneuploid hybrid speciation between Scrophularia species can occur, so hybridization and polyploidy have an important role for history of diversification. (3) The ancestral staminode type for the genus Scrophularia seems to be a large staminode. (4) Monophyly of the genus Verbascum with respect to the genus Scrophularia is strongly supported. (5) Oreosolen, is not monophyletic, because all accessions of Oreosolen were nested within Scrophularia. We discuss methods of data collection and analysis, and we describe the areas of conflict and agreement between molecular phylogenies.

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Toward a Cognitive Classical Linguistics
The Embodied Basis of Constructions in Greek and Latin
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About (k, l)-Kernels, Semikernels and Grundy Functions in Partial Line Digraphs

Abstract

Let D be a digraph of minimum in-degree at least 1. We prove that for any two natural numbers k, l such that 1 ≤ lk, the number of (k, l)-kernels of D is less than or equal to the number of (k, l)-kernels of any partial line digraph ℒD. Moreover, if l < k and the girth of D is at least l +1, then these two numbers are equal. We also prove that the number of semikernels of D is equal to the number of semikernels of ℒD. Furthermore, we introduce the concept of (k, l)-Grundy function as a generalization of the concept of Grundy function and we prove that the number of (k, l)-Grundy functions of D is equal to the number of (k, l)-Grundy functions of any partial line digraph ℒD.

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Domination Subdivision and Domination Multisubdivision Numbers of Graphs

Abstract

The domination subdivision number sd(G) of a graph G is the minimum number of edges that must be subdivided (where an edge can be subdivided at most once) in order to increase the domination number of G. It has been shown [10] that sd(T) ≤ 3 for any tree T. We prove that the decision problem of the domination subdivision number is NP-complete even for bipartite graphs. For this reason we define the domination multisubdivision number of a nonempty graph G as a minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G. We show that msd(G) ≤ 3 for any graph G. The domination subdivision number and the domination multisubdivision number of a graph are incomparable in general, but we show that for trees these two parameters are equal. We also determine the domination multisubdivision number for some classes of graphs.

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Erdős-Gallai-Type Results for Total Monochromatic Connection of Graphs

Abstract

A graph is said to be total-colored if all the edges and the vertices of the graph are colored. A total-coloring of a graph is a total monochromatically-connecting coloring (TMC-coloring, for short) if any two vertices of the graph are connected by a path whose edges and internal vertices have the same color. For a connected graph G, the total monochromatic connection number, denoted by tmc(G), is defined as the maximum number of colors used in a TMC-coloring of G. In this paper, we study two kinds of Erdős-Gallai-type problems for tmc(G) and completely solve them.

Open access
Facial Rainbow Coloring of Plane Graphs

Abstract

A vertex coloring of a plane graph G is a facial rainbow coloring if any two vertices of G connected by a facial path have distinct colors. The facial rainbow number of a plane graph G, denoted by rb(G), is the minimum number of colors that are necessary in any facial rainbow coloring of G. Let L(G) denote the order of a longest facial path in G. In the present note we prove that rb(T)32L(T) for any tree T and rb(G)53L(G) for arbitrary simple graph G. The upper bound for trees is tight. For any simple 3-connected plane graph G we have rb(G) ≤ L(G) + 5.

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Kaleidoscopic Edge-Coloring of Complete Graphs and r-Regular Graphs

Abstract

For an r-regular graph G, we define an edge-coloring c with colors from {1, 2, . . . , k}, in such a way that any vertex of G is incident with at least one edge of each color. The multiset-color cm(v) of a vertex v is defined as the ordered tuple (a 1, a 2, . . . , ak), where ai (1 ≤ ik) denotes the number of edges of color i which are incident with v in G. Then this edge-coloring c is called a k-kaleidoscopic coloring of G if every two distinct vertices in G have different multiset-colors and in this way the graph G is defined as a k-kaleidoscope. In this paper, we determine the integer k for a complete graph Kn to be a k-kaleidoscope, and hence solve a conjecture in [P. Zhang, A Kaleidoscopic View of Graph Colorings, (Springer Briefs in Math., New York, 2016)] that for any integers n and k with nk + 3 ≥ 6, the complete graph Kn is a k-kaleidoscope. Then, we construct an r-regular 3-kaleidoscope of order (2r-1)-1 − 1 for each integer r ≥ 7, where r ≡ 3 (mod 4), which solves another conjecture in [P. Zhang, A Kaleidoscopic View of Graph Colorings, (Springer Briefs in Math., New York, 2016)] on the maximum order of r-regular 3-kaleidoscopes.

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A Note on Upper Bounds for Some Generalized Folkman Numbers

Abstract

We present some new constructive upper bounds based on product graphs for generalized vertex Folkman numbers. They lead to new upper bounds for some special cases of generalized edge Folkman numbers, including the cases F e(K 3, K 4e; K 5) ≤ 27 and F e(K 4e, K 4e; K 5) ≤ 51. The latter bound follows from a construction of a K 5-free graph on 51 vertices, for which every edge coloring with two colors contains a monochromatic K 4e.

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On Decomposing the Complete Symmetric Digraph into Orientations of K 4e

Abstract

Let D be any of the 10 digraphs obtained by orienting the edges of K 4e. We establish necessary and sufficient conditions for the existence of a (Kn*, D)-design for 8 of these digraphs. Partial results as well as some nonexistence results are established for the remaining 2 digraphs.

Open access