On the connectivity of finite subset spaces

Jacob Mostovoy; Rustam Sadykov

Displaying similar documents to “On the connectivity of finite subset spaces”

On D-connected sets in the space $V^{q}$

S. Topa (1976)

Annales Polonici Mathematici

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Domination numbers in graphs with removed edge or set of edges

Magdalena Lemańska (2005)

Discussiones Mathematicae Graph Theory

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It is known that the removal of an edge from a graph G cannot decrease a domination number γ(G) and can increase it by at most one. Thus we can write that γ(G) ≤ γ(G-e) ≤ γ(G)+1 when an arbitrary edge e is removed. Here we present similar inequalities for the weakly connected domination number $γ_{w}$ and the connected domination number $γ_{c}$ , i.e., we show that $γ_{w} (G) \leq γ_{w} (G - e) \leq γ_{w} (G) + 1$ and $γ_{c} (G) \leq γ_{c} (G - e) \leq γ_{c} (G) + 2$ if G and G-e are connected. Additionally we show that $γ_{w} (G) \leq γ_{w} (G - E ₚ) \leq γ_{w} (G) + p - 1$ and $γ_{c} (G) \leq γ_{c} (G - E ₚ) \leq γ_{c} (G) + 2 p - 2$ if G and G - Eₚ are connected and Eₚ = E(Hₚ) where Hₚ of order...

On compactness and connectedness of the paratingent

Wojciech Zygmunt (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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In this note we shall prove that for a continuous function $ϕ : Δ \to ℝ^{n}$ , where $Δ \subset ℝ$ , the paratingent of $ϕ$ at $a \in Δ$ is a non-empty and compact set in $ℝ^{n}$ if and only if $ϕ$ satisfies Lipschitz condition in a neighbourhood of $a$ . Moreover, in this case the paratingent is a connected set.

On connectivity properties of hyperspaces of $R_{0}$ spaces

M. Mršević (1979)

Matematički Vesnik

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On the bounds of Laplacian eigenvalues of $k$ -connected graphs

Xiaodan Chen, Yaoping Hou (2015)

Czechoslovak Mathematical Journal

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Let $μ_{n - 1} (G)$ be the algebraic connectivity, and let $μ_{1} (G)$ be the Laplacian spectral radius of a $k$ -connected graph $G$ with $n$ vertices and $m$ edges. In this paper, we prove that $μ_{n - 1} (G) \geq \frac{2 n k^{2}}{(n (n - 1) - 2 m) (n + k - 2) + 2 k^{2}},$ with equality if and only if $G$ is the complete graph $K_{n}$ or $K_{n} - e$ . Moreover, if $G$ is non-regular, then $μ_{1} (G) < 2 Δ - \frac{2 (n Δ - 2 m) k^{2}}{2 (n Δ - 2 m) (n^{2} - 2 n + 2 k) + n k^{2}},$ where $Δ$ stands for the maximum degree of $G$ . Remark that in some cases, these two inequalities improve some previously known results.

2-factors in claw-free graphs with locally disconnected vertices

Mingqiang An, Liming Xiong, Runli Tian (2015)

Czechoslovak Mathematical Journal

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An edge of $G$ is singular if it does not lie on any triangle of $G$ ; otherwise, it is non-singular. A vertex $u$ of a graph $G$ is called locally connected if the induced subgraph $G [N (u)]$ by its neighborhood is connected; otherwise, it is called locally disconnected. In this paper, we prove that if a connected claw-free graph $G$ of order at least three satisfies the following two conditions: (i) for each locally disconnected vertex $v$ of degree at least $3$ in $G,$ there is a nonnegative integer $s$ such...

2-Cohomology of semi-simple simply connected group-schemes over curves defined over $p$ -adic fields

Jean-Claude Douai (2013)

Journal de Théorie des Nombres de Bordeaux

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Let $X$ be a proper, smooth, geometrically connected curve over a $p$ -adic field $k$ . Lichtenbaum proved that there exists a perfect duality: $Br (X) \times Pic (X) \to ℚ / ℤ$ between the Brauer and the Picard group of $X$ , from which he deduced the existence of an injection of $Br (X)$ in $\prod_{P \in X} Br (k_{P})$ where $P \in X$ and $k_{P}$ denotes the residual field of the point $P$ . The aim of this paper is to prove that if $G = \tilde{G}$ is an $X_{e t}$ - scheme of semi-simple simply connected groups (s.s.s.c groups), then we can deduce from Lichtenbaum’s results...

On a conjecture of Dekking : The sum of digits of even numbers

Iurie Boreico, Daniel El-Baz, Thomas Stoll (2014)

Journal de Théorie des Nombres de Bordeaux

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Let $q \geq 2$ and denote by $s_{q}$ the sum-of-digits function in base $q$ . For $j = 0, 1, \dots, q - 1$ consider $# {0 \leq n < N : s_{q} (2 n) \equiv j (mod q)} .$ In 1983, F. M. Dekking conjectured that this quantity is greater than $N / q$ and, respectively, less than $N / q$ for infinitely many $N$ , thereby claiming an absence of a drift (or Newman) phenomenon. In this paper we prove his conjecture.

An explicit computation of $p$ -stabilized vectors

Michitaka MIYAUCHI, Takuya YAMAUCHI (2014)

Journal de Théorie des Nombres de Bordeaux

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In this paper, we give a concrete method to compute $p$ -stabilized vectors in the space of parahori-fixed vectors for connected reductive groups over $p$ -adic fields. An application to the global setting is also discussed. In particular, we give an explicit $p$ -stabilized form of a Saito-Kurokawa lift.

Generalized 3-edge-connectivity of Cartesian product graphs

Yuefang Sun (2015)

Czechoslovak Mathematical Journal

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The generalized $k$ -connectivity $κ_{k} (G)$ of a graph $G$ was introduced by Chartrand et al. in 1984. As a natural counterpart of this concept, Li et al. in 2011 introduced the concept of generalized $k$ -edge-connectivity which is defined as $λ_{k} (G) = min {λ (S) : S \subseteq V (G)$ and $| S | = k}$ , where $λ (S)$ denotes the maximum number $ℓ$ of pairwise edge-disjoint trees $T_{1}, T_{2}, ..., T_{ℓ}$ in $G$ such that $S \subseteq V (T_{i})$ for $1 \leq i \leq ℓ$ . In this paper we prove that for any two connected graphs $G$ and $H$ we have $λ_{3} (G □ H) \geq λ_{3} (G) + λ_{3} (H)$ , where $G □ H$ is the Cartesian product of $G$ and $H$ . Moreover, the bound is sharp. We also...