A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡   ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$

Marc Coppens

Displaying similar documents to “A metric graph satisfying [...] w 4 1 = 1 $w_{4}^{1} = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 $dim (W_{4}^{1}) = 1$ ”

On the tangency of sets in generalized metric spaces for certain functions of the class $F_{ρ}^{*}$

T. Konik (1991)

Matematički Vesnik

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Maps with dimensionally restricted fibers

Vesko Valov (2011)

Colloquium Mathematicae

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We prove that if f: X → Y is a closed surjective map between metric spaces such that every fiber $f^{- 1} (y)$ belongs to a class S of spaces, then there exists an $F_{σ}$ -set A ⊂ X such that A ∈ S and $d i m f^{- 1} (y) ∖ A = 0$ for all y ∈ Y. Here, S can be one of the following classes: (i) M: e-dim M ≤ K for some CW-complex K; (ii) C-spaces; (iii) weakly infinite-dimensional spaces. We also establish that if S = M: dim M ≤ n, then dim f ∆ g ≤ 0 for almost all $g \in C (X,^{n + 1})$ .

Complete pluripolar curves and graphs

Tomas Edlund (2004)

Annales Polonici Mathematici

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It is shown that there exist $C^{\infty}$ functions on the boundary of the unit disk whose graphs are complete pluripolar. Moreover, for any natural number k, such functions are dense in the space of $C^{k}$ functions on the boundary of the unit disk. We show that this result implies that the complete pluripolar closed $C^{\infty}$ curves are dense in the space of closed $C^{k}$ curves in ℂⁿ. We also show that on each closed subset of the complex plane there is a continuous function whose graph is complete pluripolar. ...

On characterization of uniquely 3-list colorable complete multipartite graphs

Yancai Zhao, Erfang Shan (2010)

Discussiones Mathematicae Graph Theory

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For each vertex v of a graph G, if there exists a list of k colors, L(v), such that there is a unique proper coloring for G from this collection of lists, then G is called a uniquely k-list colorable graph. Ghebleh and Mahmoodian characterized uniquely 3-list colorable complete multipartite graphs except for nine graphs: $K_{2, 2, r}$ r ∈ 4,5,6,7,8, $K_{2, 3, 4}$ , $K_{1 * 4, 4}$ , $K_{1 * 4, 5}$ , $K_{1 * 5, 4}$ . Also, they conjectured that the nine graphs are not U3LC graphs. After that, except for $K_{2, 2, r}$ r ∈ 4,5,6,7,8, the others have been proved not...

Some approximate fixed point theorems without continuity of the operator using auxiliary functions

Sumit Chandok, Arslan Hojjat Ansari, Tulsi Dass Narang (2019)

Mathematica Bohemica

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We introduce partial generalized convex contractions of order $4$ and rank $4$ using some auxiliary functions. We present some results on approximate fixed points and fixed points for such class of mappings having no continuity condition in $α$ -complete metric spaces and $μ$ -complete metric spaces. Also, as an application, some fixed point results in a metric space endowed with a binary relation and some approximate fixed point results in a metric space endowed with a graph have been obtained....

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.

The nonexistence of universal metric flows

Stefan Geschke (2018)

Commentationes Mathematicae Universitatis Carolinae

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We consider dynamical systems of the form $(X, f)$ where $X$ is a compact metric space and $f : X \to X$ is either a continuous map or a homeomorphism and provide a new proof that there is no universal metric dynamical system of this kind. The same is true for metric minimal dynamical systems and for metric abstract $ω$ -limit sets, answering a question by Will Brian.

4-cycle properties for characterizing rectagraphs and hypercubes

Khadra Bouanane, Abdelhafid Berrachedi (2017)

Czechoslovak Mathematical Journal

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A $(0, 2)$ -graph is a connected graph, where each pair of vertices has either 0 or 2 common neighbours. These graphs constitute a subclass of $(0, λ)$ -graphs introduced by Mulder in 1979. A rectagraph, well known in diagram geometry, is a triangle-free $(0, 2)$ -graph. $(0, 2)$ -graphs include hypercubes, folded cube graphs and some particular graphs such as icosahedral graph, Shrikhande graph, Klein graph, Gewirtz graph, etc. In this paper, we give some local properties of 4-cycles in $(0, λ)$ -graphs and more specifically...

Remarks on $D$ -integral complete multipartite graphs

Pavel Híc, Milan Pokorný (2016)

Czechoslovak Mathematical Journal

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A graph is called distance integral (or $D$ -integral) if all eigenvalues of its distance matrix are integers. In their study of $D$ -integral complete multipartite graphs, Yang and Wang (2015) posed two questions on the existence of such graphs. We resolve these questions and present some further results on $D$ -integral complete multipartite graphs. We give the first known distance integral complete multipartite graphs $K_{p_{1}, p_{2}, p_{3}}$ with $p_{1} < p_{2} < p_{3}$ , and $K_{p_{1}, p_{2}, p_{3}, p_{4}}$ with $p_{1} < p_{2} < p_{3} < p_{4}$ , as well as the infinite classes of distance integral...

Szpilrajn type theorem for concentration dimension

Jozef Myjak, Tomasz Szarek (2002)

Fundamenta Mathematicae

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Let X be a locally compact, separable metric space. We prove that $d i m_{T} X = i n f d i m_{L} X^{'} : X^{'} i s h o m e o m o r p h i c t o X$ , where $d i m_{L} X$ and $d i m_{T} X$ stand for the concentration dimension and the topological dimension of X, respectively.

Generalized connectivity of some total graphs

Yinkui Li, Yaping Mao, Zhao Wang, Zongtian Wei (2021)

Czechoslovak Mathematical Journal

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We study the generalized $k$ -connectivity $κ_{k} (G)$ as introduced by Hager in 1985, as well as the more recently introduced generalized $k$ -edge-connectivity $λ_{k} (G)$ . We determine the exact value of $κ_{k} (G)$ and $λ_{k} (G)$ for the line graphs and total graphs of trees, unicyclic graphs, and also for complete graphs for the case $k = 3$ .

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.

Adjacent dyadic systems and the $L^{p}$ -boundedness of shift operators in metric spaces revisited

Olli Tapiola (2016)

Colloquium Mathematicae

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With the help of recent adjacent dyadic constructions by Hytönen and the author, we give an alternative proof of results of Lechner, Müller and Passenbrunner about the $L^{p}$ -boundedness of shift operators acting on functions $f \in L^{p} (X; E)$ where 1 < p < ∞, X is a metric space and E is a UMD space.

On choosability of complete multipartite graphs $K_{4, 3 * t, 2 * (k - 2 t - 2), 1 * (t + 1)}$

Guo-Ping Zheng, Yu-Fa Shen, Zuo-Li Chen, Jin-Feng Lv (2010)

Discussiones Mathematicae Graph Theory

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A graph G is said to be chromatic-choosable if ch(G) = χ(G). Ohba has conjectured that every graph G with 2χ(G)+1 or fewer vertices is chromatic-choosable. It is clear that Ohba’s conjecture is true if and only if it is true for complete multipartite graphs. In this paper we show that Ohba’s conjecture is true for complete multipartite graphs $K_{4, 3 * t, 2 * (k - 2 t - 2), 1 * (t + 1)}$ for all integers t ≥ 1 and k ≥ 2t+2, that is, $c h (K_{4, 3 * t, 2 * (k - 2 t - 2), 1 * (t + 1)}) = k$ , which extends the results $c h (K_{4, 3, 2 * (k - 4), 1 * 2}) = k$ given by Shen et al. (Discrete Math. 308 (2008) 136-143), and $c h (K_{4, 3 * 2, 2 * (k - 6), 1 * 3}) = k$ ...

Paired domination in prisms of graphs

Christina M. Mynhardt, Mark Schurch (2011)

Discussiones Mathematicae Graph Theory

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The paired domination number $γ_{p r} (G)$ of a graph G is the smallest cardinality of a dominating set S of G such that ⟨S⟩ has a perfect matching. The generalized prisms πG of G are the graphs obtained by joining the vertices of two disjoint copies of G by |V(G)| independent edges. We provide characterizations of the following three classes of graphs: $γ_{p r} (π G) = 2 γ_{p r} (G)$ for all πG; $γ_{p r} (K ₂ ☐ G) = 2 γ_{p r} (G)$ ; $γ_{p r} (K ₂ ☐ G) = γ_{p r} (G)$ .

Displaying similar documents to “A metric graph satisfying [...] w 4 1 = 1 w 4 1 = 1 that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 dim ( W 4 1 ) = 1 ”

Displaying similar documents to “A metric graph satisfying [...] w 4 1 = 1 $w_{4}^{1} = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡ ( W 4 1 ) = 1 $dim (W_{4}^{1}) = 1$ ”