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...

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.

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.

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; $γ_{p r} (K ₂ ☐ G) = 2 γ_{p r} (G)$ ; $γ_{p r} (K ₂ ☐ G) = γ_{p r} (G)$ .

Upper oriented chromatic number of undirected graphs and oriented colorings of product graphs

Éric Sopena (2012)

Discussiones Mathematicae Graph Theory

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The oriented chromatic number of an oriented graph $^{\to} G$ is the minimum order of an oriented graph $^{\to} H$ such that $^{\to} G$ admits a homomorphism to $^{\to} H$ . The oriented chromatic number of an undirected graph G is then the greatest oriented chromatic number of its orientations. In this paper, we introduce the new notion of the upper oriented chromatic number of an undirected graph G, defined as the minimum order of an oriented graph $^{\to} U$ such that every orientation $^{\to} G$ of G admits a homomorphism to $^{\to} U$ . We give...

Intrinsic linking and knotting are arbitrarily complex

Erica Flapan, Blake Mellor, Ramin Naimi (2008)

Fundamenta Mathematicae

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We show that, given any n and α, any embedding of any sufficiently large complete graph in ℝ³ contains an oriented link with components Q₁, ..., Qₙ such that for every i ≠ j, $| l k (Q_{i}, Q_{j}) | \geq α$ and $| a ₂ (Q_{i}) | \geq α$ , where $a ₂ (Q_{i})$ denotes the second coefficient of the Conway polynomial of $Q_{i}$ .

On generalized shift graphs

Christian Avart, Tomasz Łuczak, Vojtěch Rödl (2014)

Fundamenta Mathematicae

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In 1968 Erdős and Hajnal introduced shift graphs as graphs whose vertices are the k-element subsets of [n] = 1,...,n (or of an infinite cardinal κ ) and with two k-sets $A = a ₁, . . ., a_{k}$ and $B = b ₁, . . ., b_{k}$ joined if $a ₁ < a ₂ = b ₁ < a ₃ = b ₂ < \dots < a_{k} = b_{k - 1} < b_{k}$ . They determined the chromatic number of these graphs. In this paper we extend this definition and study the chromatic number of graphs defined similarly for other types of mutual position with respect to the underlying ordering. As a consequence of our result, we show the existence of a graph with...

A note on intersection dimensions of graph classes

Petr Hliněný, Aleš Kuběna (1995)

Commentationes Mathematicae Universitatis Carolinae

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The intersection dimension of a graph $G$ with respect to a class $𝒜$ of graphs is the minimum $k$ such that $G$ is the intersection of some $k$ graphs on the vertex set $V (G)$ belonging to $𝒜$ . In this paper we follow [ Kratochv’ıl J., Tuza Z.: , Graphs and Combinatorics 10 (1994), 159–168 ] and show that for some pairs of graph classes $𝒜$ , $ℬ$ the intersection dimension of graphs from $ℬ$ with respect to $𝒜$ is unbounded.

Equivalent classes for K₃-gluings of wheels

Halina Bielak (1998)

Discussiones Mathematicae Graph Theory

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In this paper, the chromaticity of K₃-gluings of two wheels is studied. For each even integer n ≥ 6 and each odd integer 3 ≤ q ≤ [n/2] all K₃-gluings of wheels $W_{q + 2}$ and $W_{n - q + 2}$ create an χ-equivalent class.

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 $dim (W_{4}^{1}) = 1$ ”