Temat: triangle-tree - Prolib Integro

Skocz do pozycji: 1.

Tytuł:: On tripartite common graphs
Autorzy:: Lee, Joonkyung
Grzesik, Andrzej
Lidický, Bernard
Volec, Jan
Opis:: A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph Kn is asymptotically minimised by the random colouring. Burr and Rosta, extending a famous conjecture of Erdős, conjectured that every graph is common. The conjectures of Erdős and of Burr and Rosta were disproved by Thomason and by Sidorenko, respectively, in the late 1980s. Collecting new examples of common graphs had not seen much progress since then, although very recently a few more graphs were verified to be common by the flag algebra method or the recent progress on Sidorenko’s conjecture. Our contribution here is to provide several new classes of tripartite common graphs. The first example is the class of so-called triangle trees, which generalises two theorems by Sidorenko and answers a question of Jagger, Šťovíček, and Thomason from 1996. We also prove that, somewhat surprisingly, given any tree T , there exists a triangle tree such that the graph obtained by adding T as a pendant tree is still common. Furthermore, we show that adding arbitrarily many apex vertices to any connected bipartite graph on at most 5 vertices yields a common graph.
Dostawca treści:: Repozytorium Uniwersytetu Jagiellońskiego

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Tytuł:: Nowhere-Zero Unoriented 6-Flows on Certain Triangular Graphs
Autorzy:: Yang, Fan
Li, Liangchen
Zhou, Sizhong
Tematy:: nowhere-zero k -flow
triangle-tree
triangle-star
bidirected graph; Pokaż więcej
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Powiązania:: https://bibliotekanauki.pl/articles/32309450.pdf Link otwiera się w nowym oknie
Opis:: A nowhere-zero unoriented flow of graph G is an assignment of non-zero real numbers to the edges of G such that the sum of the values of all edges incident with each vertex is zero. Let k be a natural number. A nowhere-zero unoriented k-flow is a flow with values from the set {±1, . . ., ±(k − 1)}, for short we call it NZ-unoriented k-flow. Let H₁ and H₂ be two graphs, H₁⊕H₂ denote the 2-sum of H₁ and H₂, if E(H₁⊕H₂) = E(H₁) ∪ E(H₂), |V(H₁)∩V(H₂)|=2, and |E(H₁)∩E(H₂)| = 1. A triangle-path in a graph G is a sequence of distinct triangles T₁, T₂, . . ., T_m in G such that for 1 ≤ i ≤ m, |E(T_i)∩E(T_i+1)| = 1 and E(T_i)∩E(T_j)=∅ if j>i+1. A triangle-star is a graph with triangles such that each triangle having one common edges with other triangles. Let G be a graph which can be partitioned into some triangle-paths or wheels H₁, H₂, . . ., H_t such that G = H₁⊕H₂⊕...⊕H_t. In this paper, we prove that G except a triangle-star admits an NZ-unoriented 6-flow. Moreover, if each H_i is a triangle-path, then G except a triangle-star admits an NZ-unoriented 5-flow.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: Numerical Presentation of the Selected Statistical Notions Based on Tukeys Concept of Observation Depth in the Sample
Wybrane pojęcia statystyczne w świetle koncepcji zanurzenia punktu w próbie - ujęcie numeryczne
Autorzy:: Wagner, Wiesław
Kobylińska, Małgorzata
Tematy:: depth measure
contour of depth
simplicial depth
the cosine method
the convex combination method
the tree triangle area method
the angular transformation method; Pokaż więcej
Wydawca:: Uniwersytet Łódzki. Wydawnictwo Uniwersytetu Łódzkiego
Powiązania:: https://bibliotekanauki.pl/articles/905269.pdf Link otwiera się w nowym oknie
Opis:: The study provides presentation of selected statistical concepts based on data depth by Tukey. The concepts as: the rang of depth, the half-space convex, contour, simplicial depth breakdown points, position numerical measures, the trimmed mean depth, regression depth and the set of generally positive points were exemplified in a two-dimensional space of the dataset. There are also given numerical algorithms in some cases to indicate already mentioned concepts and to study their affined transformation. There are also given example for a one-dimensional space besides general description
W pracy omówiono definicję zanurzenia punktu w próbie oraz wywodzące się z lej koncepcji pewne inne pojęcie statystyczne. Przedstawiono między innymi wskaźniki określające stopień zanurzenia oraz zaproponowano metody numerycznego ich wyznaczania.
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 4.

Tytuł:: Automatic simplification of the geometry of a cartographic line using contractive self-mapping – illustrated with an example of a polyline band
Autorzy:: Bac-Bronowicz, Joanna
Banasik, Piotr
Chrobak, Tadeusz
Tematy:: digital generalization
contractive self-mapping
Salichtchev’s minimum measures
geometry of a polyline in the binary tree structure
Lipschitz’s contraction triangle
Banach theorem; Pokaż więcej
Wydawca:: Oddział Kartograficzny Polskiego Towarzystwa Geograficznego
Powiązania:: https://bibliotekanauki.pl/articles/29433667.pdf Link otwiera się w nowym oknie
Opis:: The present article is another attempt to adapt map geometry to automatic digital cartography. The paper presents a method of digital polyline generalisation that uses contractive self-mapping. It is a method of simplification, not just an algorithm for simplification. This method in its 1996 version obtained a patent entitled “Method of Eliminating Points in the Process of Numerical Cartographic Generalisation” – Patent Office of the Republic of Poland, No. 181014, 1996. The first results of research conducted using the presented method, with clearly defined data (without singular points of their geometry), were published in the works of the authors in 2021 and 2022. This article presents a transition from the DLM (Digital Landscape Model) to the DCM (Digital Cartographic Model). It demonstrates an algorithm with independent solutions for the band axis and both its edges. The presented example was performed for the so-called polyline band, which can represent real topographic linear objects such as rivers and boundaries of closed areas (buildings, lakes, etc.). An unambiguous representation of both edges of the band is its axis, represented in DLM, which can be simplified to any scale. A direct consequence of this simplification is the shape of the band representing the actual shape of both edges of the object that is classified in the database as a linear object in DCM. The article presents an example performed for the so-called polyline band, which represents real topographic linear objects (roads, rivers) and area boundaries. The proposed method fulfils the following conditions: the Lipschitz condition, the Cauchy condition, the Banach theorem, and the Salichtchev’s standard for object recognition on the map. The presented method is objective in contrast to the previously used approximate methods, such as generalisations that use graph theory and fractal geometry, line smoothing and simplification algorithms, statistical methods with classification of object attributes, artificial intelligence, etc. The presented method for changing the geometry of objects by any scale of the map is 100% automatic, repeatable, and objective; that is, it does not require a cartographer’s intervention.
Dostawca treści:: Biblioteka Nauki

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