The Experts below are selected from a list of 14403 Experts worldwide ranked by ideXlab platform
J K Langley - One of the best experts on this subject based on the ideXlab platform.
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transcendental singularities for a meromorphic function with logarithmic derivative of finite lower order
Computational Methods and Function Theory, 2019Co-Authors: J K LangleyAbstract:It is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the Weaker Hypothesis that the logarithmic derivative has finite lower order.
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transcendental singularities for a meromorphic function with logarithmic derivative of finite lower order
arXiv: Complex Variables, 2018Co-Authors: J K LangleyAbstract:In this note it is shown that two key results on transcendental singularities for meromorphic functions of finite lower order have refinements which hold under the Weaker Hypothesis that the logarithmic derivative has finite lower order.
Stéphan Thomassé - One of the best experts on this subject based on the ideXlab platform.
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Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture
Combinatorica, 2019Co-Authors: Julien Bensmail, Ararat Harutyunyan, Stéphan ThomasséAbstract:In 2006, Barát and Thomassen conjectured that there is a function f such that, for every fixed tree T with t edges, every f(t)-edge-connected graph with its number of edges divisible by t has a partition of its edges into copies of T. This conjecture was recently verified by the current authors and Merker. We here further focus on the path case of the Barát-Thomassen conjecture. Before the aforementioned general proof was announced, several successive steps towards the path case of the conjecture were made, notably by Thomassen, until this particular case was totally solved by Botler, Mota, Oshiro and Wakabayashi. Our goal in this paper is to propose an alternative proof of the path case with a Weaker Hypothesis: Namely, we prove that there is a function f such that every 24-edge-connected graph with minimum degree f(t) has an edge-partition into paths of length t whenever t divides the number of edges. We also show that 24 can be dropped to 4 when the graph is eulerian.
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edge partitioning a graph into paths beyond the bar at thomassen conjecture
arXiv: Combinatorics, 2015Co-Authors: Julien Bensmail, Ararat Harutyunyan, Tiennam Le, Stéphan ThomasséAbstract:The Barat-Thomassen conjecture asserts that there is a function $f$ such that for every fixed tree $T$ with $t$ edges, every graph which is $f(t)$-edge-connected with its number of edges divisible by $t$ has a partition of its edges into copies of $T$. This has been proved in the case of paths of length $2^k$ by Thomassen, and recently shown to be true for all paths by Botler, Mota, Oshiro and Wakabayashi. Our goal in this paper is to propose an alternative proof of the path case with a Weaker Hypothesis: Namely, we prove that there is a function $f$ such that every $24$-edge-connected graph with minimum degree $f(t)$ has an edge-partition into paths of length $t$ whenever $t$ divides the number of edges. We also show that $24$ can be dropped to $4$ when the graph is eulerian.
Julien Bensmail - One of the best experts on this subject based on the ideXlab platform.
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Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture
Combinatorica, 2019Co-Authors: Julien Bensmail, Ararat Harutyunyan, Stéphan ThomasséAbstract:In 2006, Barát and Thomassen conjectured that there is a function f such that, for every fixed tree T with t edges, every f(t)-edge-connected graph with its number of edges divisible by t has a partition of its edges into copies of T. This conjecture was recently verified by the current authors and Merker. We here further focus on the path case of the Barát-Thomassen conjecture. Before the aforementioned general proof was announced, several successive steps towards the path case of the conjecture were made, notably by Thomassen, until this particular case was totally solved by Botler, Mota, Oshiro and Wakabayashi. Our goal in this paper is to propose an alternative proof of the path case with a Weaker Hypothesis: Namely, we prove that there is a function f such that every 24-edge-connected graph with minimum degree f(t) has an edge-partition into paths of length t whenever t divides the number of edges. We also show that 24 can be dropped to 4 when the graph is eulerian.
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edge partitioning a graph into paths beyond the bar at thomassen conjecture
arXiv: Combinatorics, 2015Co-Authors: Julien Bensmail, Ararat Harutyunyan, Tiennam Le, Stéphan ThomasséAbstract:The Barat-Thomassen conjecture asserts that there is a function $f$ such that for every fixed tree $T$ with $t$ edges, every graph which is $f(t)$-edge-connected with its number of edges divisible by $t$ has a partition of its edges into copies of $T$. This has been proved in the case of paths of length $2^k$ by Thomassen, and recently shown to be true for all paths by Botler, Mota, Oshiro and Wakabayashi. Our goal in this paper is to propose an alternative proof of the path case with a Weaker Hypothesis: Namely, we prove that there is a function $f$ such that every $24$-edge-connected graph with minimum degree $f(t)$ has an edge-partition into paths of length $t$ whenever $t$ divides the number of edges. We also show that $24$ can be dropped to $4$ when the graph is eulerian.
Ararat Harutyunyan - One of the best experts on this subject based on the ideXlab platform.
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Edge-partitioning a graph into paths: beyond the Barát-Thomassen conjecture
Combinatorica, 2019Co-Authors: Julien Bensmail, Ararat Harutyunyan, Stéphan ThomasséAbstract:In 2006, Barát and Thomassen conjectured that there is a function f such that, for every fixed tree T with t edges, every f(t)-edge-connected graph with its number of edges divisible by t has a partition of its edges into copies of T. This conjecture was recently verified by the current authors and Merker. We here further focus on the path case of the Barát-Thomassen conjecture. Before the aforementioned general proof was announced, several successive steps towards the path case of the conjecture were made, notably by Thomassen, until this particular case was totally solved by Botler, Mota, Oshiro and Wakabayashi. Our goal in this paper is to propose an alternative proof of the path case with a Weaker Hypothesis: Namely, we prove that there is a function f such that every 24-edge-connected graph with minimum degree f(t) has an edge-partition into paths of length t whenever t divides the number of edges. We also show that 24 can be dropped to 4 when the graph is eulerian.
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edge partitioning a graph into paths beyond the bar at thomassen conjecture
arXiv: Combinatorics, 2015Co-Authors: Julien Bensmail, Ararat Harutyunyan, Tiennam Le, Stéphan ThomasséAbstract:The Barat-Thomassen conjecture asserts that there is a function $f$ such that for every fixed tree $T$ with $t$ edges, every graph which is $f(t)$-edge-connected with its number of edges divisible by $t$ has a partition of its edges into copies of $T$. This has been proved in the case of paths of length $2^k$ by Thomassen, and recently shown to be true for all paths by Botler, Mota, Oshiro and Wakabayashi. Our goal in this paper is to propose an alternative proof of the path case with a Weaker Hypothesis: Namely, we prove that there is a function $f$ such that every $24$-edge-connected graph with minimum degree $f(t)$ has an edge-partition into paths of length $t$ whenever $t$ divides the number of edges. We also show that $24$ can be dropped to $4$ when the graph is eulerian.
Yutaka Ikeda - One of the best experts on this subject based on the ideXlab platform.
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replacing the lower curvature bound in toponogov s comparison theorem by a Weaker Hypothesis
Tohoku Mathematical Journal, 2017Co-Authors: James J Hebda, Yutaka IkedaAbstract:Toponogov's triangle comparison theorem and its generalizations are important tools for studying the topology of Riemannian manifolds. In these theorems, one assumes that the curvature of a given manifold is bounded from below by the curvature of a model surface. The models are either of constant curvature, or, in the generalizations, rotationally symmetric about some point. One concludes that geodesic triangles in the manifold correspond to geodesic triangles in the model surface which have the same corresponding side lengths, but smaller corresponding angles. In addition, a certain rigidity holds: Whenever there is equality in one of the corresponding angles, the geodesic triangle in the surface embeds totally geodesically and isometrically in the manifold. In this paper, we discuss a condition relating the geometry of a Riemannian manifold to that of a model surface which is Weaker than the usual curvature Hypothesis in the generalized Toponogov theorems, but yet is strong enough to ensure that a geodesic triangle in the manifold has a corresponding triangle in the model with the same corresponding side lengths, but smaller corresponding angles. In contrast, it is interesting that rigidity fails in this setting.
