Hereditarily indecomposable inverse limits of graphs

K. Kawamura; H. M. Tuncali; E. D. Tymchatyn

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Displaying similar documents to “Hereditarily indecomposable inverse limits of graphs”

Homeomorphisms of composants of Knaster continua

Sonja Štimac (2002)

Fundamenta Mathematicae

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The Knaster continuum $K_{p}$ is defined as the inverse limit of the pth degree tent map. On every composant of the Knaster continuum we introduce an order and we consider some special points of the composant. These are used to describe the structure of the composants. We then prove that, for any integer p ≥ 2, all composants of $K_{p}$ having no endpoints are homeomorphic. This generalizes Bandt’s result which concerns the case p = 2.

On Dimensionsgrad, resolutions, and chainable continua

Michael G. Charalambous, Jerzy Krzempek (2010)

Fundamenta Mathematicae

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For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum $S_{n, α, β}$ such that (a) $d i m S_{n, α, β} = n$ ; (b) $t r D g S_{n, α, β} = t r D g o S_{n, α, β} = α$ ; (c) $t r i n d S_{n, α, β} = t r I n d ₀ S_{n, α, β} = β$ ; (d) if β < ω(⁺), then $S_{n, α, β}$ is separable and first countable; (e) if n = 1, then $S_{n, α, β}$ can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then $S_{n, α, β}$ can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then $S_{n, α, β}$ can be made chainable and hereditarily indecomposable. In...

Singular arc-like continua

Tadeusz Maćkowiak

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CONTENTSIntroduction.......................................................................................................51. Preliminaries.................................................................................................6 A. Mappings....................................................................................................6 B. Arc-like continua.........................................................................................8 C. Pseudosuspensions...................................................................................8 D....

Unicyclic graphs with bicyclic inverses

Swarup Kumar Panda (2017)

Czechoslovak Mathematical Journal

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A graph is nonsingular if its adjacency matrix $A (G)$ is nonsingular. The inverse of a nonsingular graph $G$ is a graph whose adjacency matrix is similar to $A {(G)}^{- 1}$ via a particular type of similarity. Let $ℋ$ denote the class of connected bipartite graphs with unique perfect matchings. Tifenbach and Kirkland (2009) characterized the unicyclic graphs in $ℋ$ which possess unicyclic inverses. We present a characterization of unicyclic graphs in $ℋ$ which possess bicyclic inverses.

On the hyperspace $C_{n} (X) / {C_{n}}_{K} (X)$

José G. Anaya, Enrique Castañeda-Alvarado, José A. Martínez-Cortez (2021)

Commentationes Mathematicae Universitatis Carolinae

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Let $X$ be a continuum and $n$ a positive integer. Let $C_{n} (X)$ be the hyperspace of all nonempty closed subsets of $X$ with at most $n$ components, endowed with the Hausdorff metric. For $K$ compact subset of $X$ , define the hyperspace ${C_{n}}_{K} (X) = {A \in C_{n} (X) : K \subset A}$ . In this paper, we consider the hyperspace $C_{K}^{n} (X) = C_{n} (X) / {C_{n}}_{K} (X)$ , which can be a tool to study the space $C_{n} (X)$ . We study this hyperspace in the class of finite graphs and in general, we prove some properties such as: aposyndesis, local connectedness, arcwise disconnectedness, and contractibility. ...

Arcwise accessibility in hyperspaces

Sam B. Nadler, Jr.

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CONTENTS1. Introduction........................................................................................................ 52. Segmentwise accessibility..................................................................................... 73. Arcwise accessibility of singletons....................................................................... 84. Compacta in X which arcwise disconnect $2^{X}$ or C(X)................................ 155. Hereditary indecomposability and arcwise accessibility.....................................

A continuum $X$ such that $C (X)$ is not continuously homogeneous

Alejandro Illanes (2016)

Commentationes Mathematicae Universitatis Carolinae

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A metric continuum $X$ is said to be continuously homogeneous provided that for every two points $p, q \in X$ there exists a continuous surjective function $f : X \to X$ such that $f (p) = q$ . Answering a question by W.J. Charatonik and Z. Garncarek, in this paper we show a continuum $X$ such that the hyperspace of subcontinua of $X$ , $C (X)$ , is not continuously homogeneous.

Making holes in the cone, suspension and hyperspaces of some continua

José G. Anaya, Enrique Castañeda-Alvarado, Alejandro Fuentes-Montes de Oca, Fernando Orozco-Zitli (2018)

Commentationes Mathematicae Universitatis Carolinae

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A connected topological space $Z$ is unicoherent provided that if $Z = A \cup B$ where $A$ and $B$ are closed connected subsets of $Z$ , then $A \cap B$ is connected. Let $Z$ be a unicoherent space, we say that $z \in Z$ makes a hole in $Z$ if $Z - {z}$ is not unicoherent. In this work the elements that make a hole to the cone and the suspension of a metric space are characterized. We apply this to give the classification of the elements of hyperspaces of some continua that make them hole.

On 𝓕-independence in graphs

Frank Göring, Jochen Harant, Dieter Rautenbach, Ingo Schiermeyer (2009)

Discussiones Mathematicae Graph Theory

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Let be a set of graphs and for a graph G let $α_{} (G)$ and $α *_{} (G)$ denote the maximum order of an induced subgraph of G which does not contain a graph in as a subgraph and which does not contain a graph in as an induced subgraph, respectively. Lower bounds on $α_{} (G)$ and $α *_{} (G)$ are presented.

On the classification of inverse limits of tent maps

Louis Block, Slagjana Jakimovik, Lois Kailhofer, James Keesling (2005)

Fundamenta Mathematicae

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Let $f_{s}$ and $f_{t}$ be tent maps on the unit interval. In this paper we give a new proof of the fact that if the critical points of $f_{s}$ and $f_{t}$ are periodic and the inverse limit spaces $(I, f_{s})$ and $(I, f_{t})$ are homeomorphic, then s = t. This theorem was first proved by Kailhofer. The new proof in this paper simplifies the proof of Kailhofer. Using the techniques of the paper we are also able to identify certain isotopies between homeomorphisms on the inverse limit space.

Extending generalized Whitney maps

Ivan Lončar (2017)

Archivum Mathematicum

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For metrizable continua, there exists the well-known notion of a Whitney map. If $X$ is a nonempty, compact, and metric space, then any Whitney map for any closed subset of $2^{X}$ can be extended to a Whitney map for $2^{X}$ [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

Proper connection number of bipartite graphs

Jun Yue, Meiqin Wei, Yan Zhao (2018)

Czechoslovak Mathematical Journal

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An edge-colored graph $G$ is proper connected if every pair of vertices is connected by a proper path. The proper connection number of a connected graph $G$ , denoted by $pc (G)$ , is the smallest number of colors that are needed to color the edges of $G$ in order to make it proper connected. In this paper, we obtain the sharp upper bound for $pc (G)$ of a general bipartite graph $G$ and a series of extremal graphs. Additionally, we give a proper $2$ -coloring for a connected bipartite graph $G$ having $δ (G) \geq 2$ and a dominating...

The extremal irregularity of connected graphs with given number of pendant vertices

Xiaoqian Liu, Xiaodan Chen, Junli Hu, Qiuyun Zhu (2022)

Czechoslovak Mathematical Journal

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The irregularity of a graph $G = (V, E)$ is defined as the sum of imbalances $| d_{u} - d_{v} |$ over all edges $u v \in E$ , where $d_{u}$ denotes the degree of the vertex $u$ in $G$ . This graph invariant, introduced by Albertson in 1997, is a measure of the defect of regularity of a graph. In this paper, we completely determine the extremal values of the irregularity of connected graphs with $n$ vertices and $p$ pendant vertices ( $1 \leq p \leq n - 1$ ), and characterize the corresponding extremal graphs.

Global continuum of positive solutions for discrete $p$ -Laplacian eigenvalue problems

Dingyong Bai, Yuming Chen (2015)

Applications of Mathematics

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We discuss the discrete $p$ -Laplacian eigenvalue problem, $\{\begin{matrix} Δ (φ_{p} (Δ u (k - 1))) + λ a (k) g (u (k)) = 0, k \in {1, 2, ..., T}, \\ u (0) = u (T + 1) = 0, \end{matrix}$ where $T > 1$ is a given positive integer and $φ_{p} (x) : = {| x |}^{p - 2} x$ , $p > 1$ . First, the existence of an unbounded continuum $𝒞$ of positive solutions emanating from $(λ, u) = (0, 0)$ is shown under suitable conditions on the nonlinearity. Then, under an additional condition, it is shown that the positive solution is unique for any $λ > 0$ and all solutions are ordered. Thus the continuum $𝒞$ is a monotone continuous curve globally defined for all $λ > 0$ .