The Experts below are selected from a list of 684 Experts worldwide ranked by ideXlab platform
Taraz Anusch - One of the best experts on this subject based on the ideXlab platform.
-
The bandwidth theorem in sparse graphs
'Alliance of Diamond Open Access Journals', 2020Co-Authors: Allen Peter, Böttcher Julia, Ehrenmüller Julia, Taraz AnuschAbstract:The bandwidth theorem [Mathematische Annalen, 343(1):175–205, 2009] states that any n-vertex graph G with minimum degree [Formula Presented] contains all n-vertex k-colourable graphs H with bounded maximum degree and bandwidth o(n). We provide sparse analogues of this statement in random graphs as well as pseudorandom graphs. More precisely, we show that for p ≫[Formula Presented] asymptotically almost surely each spanning subgraph G of G(n, p) with minimum degree [Formula Presented] pn contains all n-vertex k-colourable graphs H with maximum degree ∆, bandwidth o(n), and at least Cp−2 vertices not contained in any triangle. A similar result is shown for sufficiently bijumbled graphs, which, to the best of our knowledge, is the first resilience result in pseudorandom graphs for a rich class of spanning subgraphs. Finally, we provide improved results for H with small degeneracy, which in particular imply a resilience result in G(n, p) with respect to the containment of spanning bounded degree trees for p ≫[Formula Presented]
-
The Bandwidth Theorem in Sparse Graphs
2020Co-Authors: Allen Peter, Böttcher Julia, Ehrenmüller Julia, Taraz AnuschAbstract:The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$-vertex graph $G$ with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)n$ contains all $n$-vertex $k$-colourable graphs $H$ with bounded maximum degree and bandwidth $o(n)$. We provide sparse analogues of this statement in random graphs as well as pseudorandom graphs. More precisely, we show that for $p\gg \big(\tfrac{\log n}{n}\big)^{1/\Delta}$ asymptotically almost surely each spanning subgraph $G$ of $G(n,p)$ with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)pn$ contains all $n$-vertex $k$-colourable graphs $H$ with maximum degree $\Delta$, bandwidth $o(n)$, and at least $C p^{-2}$ vertices not contained in any triangle. A similar result is shown for sufficiently bijumbled graphs, which, to the best of our knowledge, is the first resilience result in pseudorandom graphs for a rich class of spanning subgraphs. Finally, we provide improved results for $H$ with small degeneracy, which in particular imply a resilience result in $G(n,p)$ with respect to the containment of spanning bounded degree trees for $p\gg \big(\tfrac{\log n}{n}\big)^{1/3}$.Comment: 60 page
-
A spanning bandwidth theorem in random graphs
2019Co-Authors: Allen Peter, Böttcher Julia, Ehrenmüller Julia, Schnitzer Jakob, Taraz AnuschAbstract:The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$-vertex graph $G$ with minimum degree $(\frac{k-1}{k}+o(1))n$ contains all $n$-vertex $k$-colourable graphs $H$ with bounded maximum degree and bandwidth $o(n)$. In [arXiv:1612.00661] a random graph analogue of this statement is proved: for $p\gg (\frac{\log n}{n})^{1/\Delta}$ a.a.s. each spanning subgraph $G$ of $G(n,p)$ with minimum degree $(\frac{k-1}{k}+o(1))pn$ contains all $n$-vertex $k$-colourable graphs $H$ with maximum degree $\Delta$, bandwidth $o(n)$, and at least $C p^{-2}$ vertices not contained in any triangle. This restriction on vertices in triangles is necessary, but limiting. In this paper we consider how it can be avoided. A special case of our main result is that, under the same conditions, if additionally all vertex neighbourhoods in $G$ contain many copies of $K_\Delta$ then we can drop the restriction on $H$ that $Cp^{-2}$ vertices should not be in triangles.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1612.0066
-
Spanning embeddings of arrangeable graphs with sublinear bandwidth
'Wiley', 2015Co-Authors: Böttcher Julia, Taraz Anusch, Würfl AndreasAbstract:The Bandwidth Theorem of Böttcher, et al. [Mathematische Annalen 343 (2009), 175–205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this result to a-arrangeable graphs H with inline image, where n is the number of vertices of H. Our result implies that sufficiently large n-vertex graphs G with minimum degree at least inline image contain almost all planar graphs on n vertices as subgraphs. Using techniques developed by Allen, et al. [Combinatorica 33 (2013), 125–160] we can also apply our methods to show that almost all planar graphs H have Ramsey number at most inline image. We obtain corresponding results for graphs embeddable on different orientable surface
-
Spanning embeddings of arrangeable graphs with sublinear bandwidth
2013Co-Authors: Böttcher Julia, Taraz Anusch, Würfl AndreasAbstract:The Bandwidth Theorem of B\"ottcher, Schacht and Taraz [Mathematische Annalen 343 (1), 175-205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this result to a-arrangeable graphs H with \Delta(H)
Böttcher Julia - One of the best experts on this subject based on the ideXlab platform.
-
The bandwidth theorem in sparse graphs
'Alliance of Diamond Open Access Journals', 2020Co-Authors: Allen Peter, Böttcher Julia, Ehrenmüller Julia, Taraz AnuschAbstract:The bandwidth theorem [Mathematische Annalen, 343(1):175–205, 2009] states that any n-vertex graph G with minimum degree [Formula Presented] contains all n-vertex k-colourable graphs H with bounded maximum degree and bandwidth o(n). We provide sparse analogues of this statement in random graphs as well as pseudorandom graphs. More precisely, we show that for p ≫[Formula Presented] asymptotically almost surely each spanning subgraph G of G(n, p) with minimum degree [Formula Presented] pn contains all n-vertex k-colourable graphs H with maximum degree ∆, bandwidth o(n), and at least Cp−2 vertices not contained in any triangle. A similar result is shown for sufficiently bijumbled graphs, which, to the best of our knowledge, is the first resilience result in pseudorandom graphs for a rich class of spanning subgraphs. Finally, we provide improved results for H with small degeneracy, which in particular imply a resilience result in G(n, p) with respect to the containment of spanning bounded degree trees for p ≫[Formula Presented]
-
The Bandwidth Theorem in Sparse Graphs
2020Co-Authors: Allen Peter, Böttcher Julia, Ehrenmüller Julia, Taraz AnuschAbstract:The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$-vertex graph $G$ with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)n$ contains all $n$-vertex $k$-colourable graphs $H$ with bounded maximum degree and bandwidth $o(n)$. We provide sparse analogues of this statement in random graphs as well as pseudorandom graphs. More precisely, we show that for $p\gg \big(\tfrac{\log n}{n}\big)^{1/\Delta}$ asymptotically almost surely each spanning subgraph $G$ of $G(n,p)$ with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)pn$ contains all $n$-vertex $k$-colourable graphs $H$ with maximum degree $\Delta$, bandwidth $o(n)$, and at least $C p^{-2}$ vertices not contained in any triangle. A similar result is shown for sufficiently bijumbled graphs, which, to the best of our knowledge, is the first resilience result in pseudorandom graphs for a rich class of spanning subgraphs. Finally, we provide improved results for $H$ with small degeneracy, which in particular imply a resilience result in $G(n,p)$ with respect to the containment of spanning bounded degree trees for $p\gg \big(\tfrac{\log n}{n}\big)^{1/3}$.Comment: 60 page
-
A spanning bandwidth theorem in random graphs
2019Co-Authors: Allen Peter, Böttcher Julia, Ehrenmüller Julia, Schnitzer Jakob, Taraz AnuschAbstract:The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$-vertex graph $G$ with minimum degree $(\frac{k-1}{k}+o(1))n$ contains all $n$-vertex $k$-colourable graphs $H$ with bounded maximum degree and bandwidth $o(n)$. In [arXiv:1612.00661] a random graph analogue of this statement is proved: for $p\gg (\frac{\log n}{n})^{1/\Delta}$ a.a.s. each spanning subgraph $G$ of $G(n,p)$ with minimum degree $(\frac{k-1}{k}+o(1))pn$ contains all $n$-vertex $k$-colourable graphs $H$ with maximum degree $\Delta$, bandwidth $o(n)$, and at least $C p^{-2}$ vertices not contained in any triangle. This restriction on vertices in triangles is necessary, but limiting. In this paper we consider how it can be avoided. A special case of our main result is that, under the same conditions, if additionally all vertex neighbourhoods in $G$ contain many copies of $K_\Delta$ then we can drop the restriction on $H$ that $Cp^{-2}$ vertices should not be in triangles.Comment: 26 pages. arXiv admin note: text overlap with arXiv:1612.0066
-
Spanning embeddings of arrangeable graphs with sublinear bandwidth
'Wiley', 2015Co-Authors: Böttcher Julia, Taraz Anusch, Würfl AndreasAbstract:The Bandwidth Theorem of Böttcher, et al. [Mathematische Annalen 343 (2009), 175–205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this result to a-arrangeable graphs H with inline image, where n is the number of vertices of H. Our result implies that sufficiently large n-vertex graphs G with minimum degree at least inline image contain almost all planar graphs on n vertices as subgraphs. Using techniques developed by Allen, et al. [Combinatorica 33 (2013), 125–160] we can also apply our methods to show that almost all planar graphs H have Ramsey number at most inline image. We obtain corresponding results for graphs embeddable on different orientable surface
-
Spanning embeddings of arrangeable graphs with sublinear bandwidth
2013Co-Authors: Böttcher Julia, Taraz Anusch, Würfl AndreasAbstract:The Bandwidth Theorem of B\"ottcher, Schacht and Taraz [Mathematische Annalen 343 (1), 175-205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this result to a-arrangeable graphs H with \Delta(H)
Hansen Wolfhard - One of the best experts on this subject based on the ideXlab platform.
-
On the existence of Evans potentials
'Springer Science and Business Media LLC', 2013Co-Authors: Hansen Wolfhard, Netuka IvanAbstract:Hansen W, Netuka I. On the existence of Evans potentials. Mathematische Annalen. 2013;356(4):1283-1302.It is shown that, for every noncompact parabolic Riemannian manifold and every nonpolar compact in , there exists a positive harmonic function on which tends to at infinity. (This is trivial for , easy for , and known for parabolic Riemann surfaces.) In fact, the statement is proven, more generally, for any noncompact connected Brelot harmonic space , where constants are the only positive superharmonic functions and, for every nonpolar compact set , there is a symmetric (positive) Green function for . This includes the case of parabolic Riemannian manifolds. Without symmetry, however, the statement may fail. This is shown by an example, where the underlying space is a graph (the union of the parallel half-lines , and the line segments )
-
One-radius results for supermedian functions on R-d, d
'Springer Science and Business Media LLC', 2010Co-Authors: Hansen Wolfhard, Nikolov NikolaiAbstract:Hansen W, Nikolov N. One-radius results for supermedian functions on R-d, d <= 2. Mathematische Annalen. 2010;348(3):565-575.A classical result states that every lower bounded superharmonic function on R-2 is constant. In this paper the following (stronger) one-circle version is proven. If f : R-2 --> (-infinity, infinity] is lower semicontinuous, lim inf(|x| --> infinity) f (x)/ln |x| >= 0, and, for every x --> R-2, 1/(2 pi) integral(2 pi)(0) f (x + r (x)e(it)) dt (0,infinity) is continuous, sup(x)is an element of(R2) (r (x) - |x|) < infinity, and inf(x is an element of R2) (r (x) - |x|) = -infinity, then f is constant. Moreover, it is shown that, assuming r
-
Global comparison of perturbed Green functions
'Springer Science and Business Media LLC', 2006Co-Authors: Hansen WolfhardAbstract:Hansen W. Global comparison of perturbed Green functions. Mathematische Annalen. 2006;334(3):643-678.Given a Green function G (e.g. with respect to (-Delta)(alpha/2), 0 < alpha
-
Boundary sets where harmonic functions may become infinite
'Springer Science and Business Media LLC', 2002Co-Authors: Gardiner, Stephen J., Hansen WolfhardAbstract:Gardiner SJ, Hansen W. Boundary sets where harmonic functions may become infinite. Mathematische Annalen. 2002;323(1):41-54.This paper characterizes the subsets E of R-n which have the following property: there exists a harmonic function u on R-n x (0, + infinity) such that u(x, t) --> +infinity as t --> 0+ for each x in E. This problem has its roots in classical work of Lusin and Privalov, and the answer has been known for some time in the case where n = 1. However, the characterization turns out to be more delicate in higher dimensions
-
Continuity of eigenvalues for Schrödinger operators, $L^p$-properties of Kato type integral operators
'Springer Science and Business Media LLC', 2001Co-Authors: Ben Amor Ali, Hansen WolfhardAbstract:Ben Amor A, Hansen W. Continuity of eigenvalues for Schrödinger operators, $L^p$-properties of Kato type integral operators. Mathematische Annalen. 2001;321(4):925-953.Given an arbitrary relatively compact (finely) open subset of R-d, mu-eigenvalues of -A (D) + nu are studied where A (D) is the Dirichlet Laplacian on D and mu, V are measures on R-d such that G(X)(mu) is continuous and G(X)(nu) is bounded for every ball X in R-d (G(X) being Green's function for X). Moreover, it is shown that these eigenvalues depend continuously on D and nu. The results are based on very general compactness and convergence properties of integral operators of Kato type which are developed before
Brochard Sylvain - One of the best experts on this subject based on the ideXlab platform.
-
Champs alg\'ebriques et foncteur de Picard
2008Co-Authors: Brochard SylvainAbstract:This text is my thesis, defended in June 2007, in the status it was at this time. The most important results are contained in the article "Foncteur de Picard d'un champ alg\'ebrique" to appear in "Mathematische Annalen" (see the preprint arXiv:0711.4545). In the article, some results have been added, and some previous results have been strengthened. However, the proofs of the results contained in the appendix (concerning the smooth-\'etale cohomology on an algebraic stack) have been removed. The thesis is only put on the ArXiv to provide a more lasting reference than my webpage for these proofs
-
Champs alg\'ebriques et foncteur de Picard
2008Co-Authors: Brochard SylvainAbstract:This text is my thesis, defended in June 2007, in the status it was at this time. The most important results are contained in the article "Foncteur de Picard d'un champ alg\'ebrique" to appear in "Mathematische Annalen" (see the preprint arXiv:0711.4545). In the article, some results have been added, and some previous results have been strengthened. However, the proofs of the results contained in the appendix (concerning the smooth-\'etale cohomology on an algebraic stack) have been removed. The thesis is only put on the ArXiv to provide a more lasting reference than my webpage for these proofs.Comment: Thesis, June 2007, 108 pages, to serve as a reference for another articl
Zedda Michela - One of the best experts on this subject based on the ideXlab platform.
-
Balanced metrics on Cartan and Cartan–Hartogs domains
'Springer Science and Business Media LLC', 2012Co-Authors: Loi Andrea, Zedda MichelaAbstract:This paper consists of two results dealing with balanced metrics (in Donaldson terminology) on noncompact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in Loi and Zedda (Mathematische Annalen, 2011) we also provide the first example of complete, Kähler-Einstein and projectively induced metric g such that αg is not balanced for all α > 0
-
Balanced metrics on Cartan and Cartan-Hartogs domains
'Springer Science and Business Media LLC', 2010Co-Authors: Loi Andrea, Zedda MichelaAbstract:This paper consists of two results dealing with balanced metrics (in S. Donaldson terminology) on nonconpact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in [13] (Kaehler-Einstein submanifolds of the infinite dimensional projective space, to appear in Mathematische Annalen) we also provide the first example of complete, Kaehler-Einstein and projectively induced metric g such that $\alpha g$ is not balanced for all $\alpha >0$.Comment: 11 page