scholarly journals Chordal and Sequentially Cohen-Macaulay Clutters

10.37236/695 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Russ Woodroofe
Keyword(s):  
Chordal Graphs ◽  
Geometric Properties ◽  
Linear Resolution ◽  
Independence Complex ◽  
Definition Of

We extend the definition of chordal from graphs to clutters. The resulting family generalizes both chordal graphs and matroids, and obeys many of the same algebraic and geometric properties. Specifically, the independence complex of a chordal clutter is shellable, hence sequentially Cohen-Macaulay; and the circuit ideal of a certain complement to such a clutter has a linear resolution. Minimal non-chordal clutters are also closely related to obstructions to shellability, and we give some general families of such obstructions, together with a classification by computation of all obstructions to shellability on 6 vertices.

scholarly journals Convexity of hesitant fuzzy sets based on aggregation functions

2020 ◽  
pp. 45-45
Author(s):  
Pedro Huidobro ◽  
Pedro Alonso ◽  
Vladimír Janis ◽  
Susana Montes
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Fuzzy Optimization ◽  
Hesitant Fuzzy Set ◽  
Hesitant Fuzzy Sets ◽  
Geometric Properties ◽  
Aggregation Functions ◽  
Definition Of

Convexity is one of the most important geometric properties of sets and a useful concept in many fields of mathematics, like optimization. As there are also important applications making use of fuzzy optimization, it is obvious that the studies of convexity are also frequent. In this paper we have extended the notion of convexity for hesitant fuzzy sets in order to fulfill some necessary properties. Namely, we have found an appropriate definition of convexity for hesitant fuzzy sets on any ordered universe based on aggregation functions such that it is compatible with the intersection, that is, the intersection of two convex hesitant fuzzy sets is a convex hesitant fuzzy set and it fulfills the cut worthy property.

scholarly journals A class of hypergraphs that generalizes chordal graphs

2010 ◽  
Vol 106 (1) ◽  
pp. 50 ◽  
Author(s):  
Eric Emtander
Keyword(s):  
Simplicial Complexes ◽  
Natural Generalization ◽  
Chordal Graphs ◽  
Graph Algebras ◽  
Higher Dimensional ◽  
Dimensional Version ◽  
Definition Of ◽  
Flag Complexes ◽  
Circuit Graph

In this paper we introduce a class of hypergraphs that we call chordal. We also extend the definition of triangulated hypergraphs, given by H. T. Hà and A. Van Tuyl, so that a triangulated hypergraph, according to our definition, is a natural generalization of a chordal (rigid circuit) graph. R. Fröberg has showed that the chordal graphs corresponds to graph algebras, $R/I(\mathcal{G})$, with linear resolutions. We extend Fröberg's method and show that the hypergraph algebras of generalized chordal hypergraphs, a class of hypergraphs that includes the chordal hypergraphs, have linear resolutions. The definitions we give, yield a natural higher dimensional version of the well known flag property of simplicial complexes. We obtain what we call $d$-flag complexes.

scholarly journals A Note on Independence Complexes of Chordal Graphs and Dismantling

10.37236/5571 ◽  
2017 ◽  
Vol 24 (2) ◽  
Author(s):  
Michał Adamaszek
Keyword(s):  
Chordal Graph ◽  
Chordal Graphs ◽  
Homotopy Equivalent ◽  
Tree Models ◽  
Independence Complex

We show that the independence complex of a chordal graph is contractible if and only if this complex is dismantlable (strong collapsible) and it is homotopy equivalent to a sphere if and only if its core is a cross-polytopal sphere. The proof uses the properties of tree models of chordal graphs.

scholarly journals Collapsibility of Non-Cover Complexes of Graphs

10.37236/8684 ◽  
2020 ◽  
Vol 27 (1) ◽  
Author(s):  
Ilkyoo Choi ◽  
Jinha Kim ◽  
Boram Park
Keyword(s):  
Simplicial Complex ◽  
Domination Number ◽  
Independent Set ◽  
Chordal Graphs ◽  
Alexander Dual ◽  
Vertex Set ◽  
Independence Complex ◽  
Independence Domination Number

Let $G$ be a graph on the vertex set $V$. A vertex subset $W \subseteq V$ is a cover of $G$ if $V \setminus W$ is an independent set of $G$, and $W$ is a non-cover of $G$ if $W$ is not a cover of $G$. The non-cover complex of $G$ is a simplicial complex on $V$ whose faces are non-covers of $G$. Then the non-cover complex of $G$ is the combinatorial Alexander dual of the independence complex of $G$. Aharoni asked if the non-cover complex of a graph $G$ without isolated vertices is $(|V(G)|-i\gamma(G)-1)$-collapsible where $i\gamma(G)$ denotes the independence domination number of $G$. Extending a result by the second author, who verified Aharoni's question in the affirmative for chordal graphs, we prove that the answer to the question is yes for all graphs.

scholarly journals On the hyperbolicity of edge-chordal and path-chordal graphs

Filomat ◽  
2016 ◽  
Vol 30 (9) ◽  
pp. 2599-2607 ◽  
Author(s):  
Sergio Bermudo ◽  
Walter Carballosa ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Chordal Graph ◽  
Chordal Graphs ◽  
Gromov Hyperbolicity ◽  
Geodesic Triangle ◽  
Geodesic Metric Space ◽  
Geodesic Metric ◽  
Hyperbolic Graph ◽  
Hyperbolic Graphs ◽  
Definition Of ◽  
Two Sides

If X is a geodesic metric space and x1, x2, x3 ( X, a geodesic triangle T = {x1, x2, x3} is the union of the three geodesics [x1x2], [x2x3] and [x3x1] in X. The space X is ?-hyperbolic (in the Gromov sense) if any side of T is contained in a ?-neighborhood of the union of the other two sides, for every geodesic triangle T in X. An important problem in the study of hyperbolic graphs is to relate the hyperbolicity with some classical properties in graph theory. In this paper we find a very close connection between hyperbolicity and chordality: we extend the classical definition of chordality in two ways, edge-chordality and path-chordality, in order to relate this propertywith Gromov hyperbolicity. In fact, we prove that every edge-chordal graph is hyperbolic and that every hyperbolic graph is path-chordal. Furthermore, we prove that every path-chordal cubic graph with small path-chordality constant is hyperbolic.

ON GEOMETRIC PROPERTIES OF SPHERICAL CONICS AND GENERALIZATION OF Π IN NAVIGATION AND MAPPING

2012 ◽  
Vol 38 (4) ◽  
pp. 141-151 ◽  
Author(s):  
Piotr Kopacz
Keyword(s):  
Euclidean Plane ◽  
Curved Surfaces ◽  
Comparison Analysis ◽  
Global Approximation ◽  
Plane Model ◽  
Geometric Properties ◽  
Applied Model ◽  
Dimensional Modeling ◽  
Definition Of ◽  
Geometric Definition

First, we cover the conical curves on 2-dimensional modeling sphere S 2 showing their geometric properties affecting the hyperbolic navigation. We place emphasis on the geometric definition of spherical parabola and relate it to the notions of spherical ellipse and hyperbola and give simple geometric proofs for relations between conical curves on the sphere. In the second part of the paper function representing the ratio of the circle's circumference to its diameter has been defined and researched to analyze the potential discrepancies in the spherical and conical projective models on which the navigational computations are based on. We compare some non-Euclidean geometric properties of curved surfaces and its Euclidean plane model in reference to the local and global approximation. As a working tool we use function for geometric comparison analysis in the theory of long-range navigation and cartographic projection. We state the existence of the infinite number of the circles having the same radius but different circumference on the conical surface. Finally, we survey the exemplary proposals of generalization of function . In particular, we focus on the geometric structure of applied model treated as a metric space showing the differences in the outputting computations if the changes in a metric are made. We also relate the function to Tissot's indicatrix of distortion.

scholarly journals Radio Properties of Active Nearby Spiral Galaxies

1978 ◽  
Vol 77 ◽  
pp. 205-219 ◽  
Author(s):  
A. G. de Bruyn
Keyword(s):  
Spiral Galaxies ◽  
Surrounding Medium ◽  
Seyfert Galaxies ◽  
Point Of View ◽  
Physical Situation ◽  
Working Definition ◽  
Linear Resolution ◽  
Distant Galaxies ◽  
Nearby Galaxies ◽  
Definition Of

Before reviewing the radio properties of active spiral galaxies it is appropriate, as well as instructive, to think about a working definition of an active galaxy. This may seem a trivial point when we consider classes of objects like Seyfert galaxies or radio galaxies but this is much less so when we inspect the nearby systems. In a sample of nearby galaxies one is likely to encounter much more milder forms of activity than that known from studies of more distant galaxies. This is, of course, due to the fact that the latter have been selectively taken from a much larger reservoir of objects. (Although this may seem a disadvantage from an observational point of view, there are some clear advantages as well. Firstly, we can obtain a much better linear resolution once we have been able to isolate the active nearby galaxies and, secondly, we eventually may hope to learn more about the physical situation that existed prior to the onset of the active period and how the surrounding medium reacts to the activity.)

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

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