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Page 1718 of Mathematical Reviews Vol. , Issue 2004c [page]

2004 Mathematical Reviews  
Thomas Andreae (D-HAMB; Hamburg) 2004c:05109 05C40 Diestel, Reinhard (D-HAMB-SM; Hamburg) The countable Erdés-Menger conjecture with ends. (English summary) Dedicated to Crispin St. J. A.  ...  The author proves, for countable graphs G, the extension of this conjecture in which the sets A, B and X are allowed to contain ends as well as vertices, and where the closure of A avoids B and vice versa  ... 

Page 4624 of Mathematical Reviews Vol. , Issue 90H [page]

1990 Mathematical Reviews  
. (4) (.%,, 0”) is complete. (5) (.%, p™) is convex in the sense of Menger.  ...  After some observations concerning the paucity of results on long-standing and very natural conjectures (mostly by Erdés), which they opine could be due to the fact “that very few sym- metric patterns  ... 

Page 1341 of Mathematical Reviews Vol. , Issue 85d [page]

1985 Mathematical Reviews  
Erdés conjectured the following extension of Menger’s theorem: Let A, B be nonempty disjoint sets of vertices in a graph G; then there exist a system P of disjoint A, B-paths in G and a set S of vertices  ...  The author proves this conjecture for graphs without infinite paths, as well as for locally finite graphs having no subdivision of the dyadic tree as a subgraph and in which no end contains an infinite  ... 

Enlarging vertex-flames in countable digraphs [article]

Joshua Erde, J. Pascal Gollin, Attila Joó
2021 arXiv   pre-print
A structural generalisation of vertex-flames and largeness to infinite digraphs was given by the third author and the analogue of Lovász' result for countable digraphs was shown.  ...  the root.  ...  By continuing the construction recursively we end up with infinitely many pairwise distinct s n ∈ V (P ) which is a contradiction.  ... 
arXiv:2003.06178v2 fatcat:b7lm6gkdljah5hmj2tjmqb53ry

Large vertex-flames in uncountable digraphs [article]

Florian Gut, Attila Joó
2022 arXiv   pre-print
The positive result for countably infinite digraphs based on this structural infinite generalisation were obtained by the second author.  ...  A spanning subdigraph L of D with κ_L(r,v)=κ_D(r,v) for every v∈ V-r must have at least ∑_v∈ V-rκ_D(r,v) edges.  ...  Erdős conjectured the following structural infinite generalisation of Menger's theorem (it was known as the Erdős-Menger conjecture) which was eventually proved after several partial results by Aharoni  ... 
arXiv:2107.12935v3 fatcat:rwhktnij5jex5kqdsxy5f44cgm

Page 575 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
Musiat) 2004h:46043 46G10 (28B05, 46B99) Diestel, Reinhard The countable Erdés-Menger conjecture with ends. (English summary) Dedicated to Crispin St. J. A. Nash-Wiliiams. J. Combin. Theory Ser.  ...  of the Erdés-Ginzburg-Ziv theorem.  ... 

Hausdorff dimension, projections, and the Fourier transform

P. Mattila
2004 Publicacions matemàtiques  
With new tools and the results of Mel'nikov in [Me] , this question can be asked without any reference to analytic functions: Let c(x, y, z) be the Menger curvature of the triple x, y, z ∈ R 2 .  ...  Let µ be the countable product of the measures 1 2 (δ {1} + δ {−1} ).  ...  Find a new proof for Besicovitch's projection theorem for purely unrectifiable sets with H 1 (A) < ∞ that would give some quantitative estimates, for example for π 0 L 1 (p θ (A(ε))) dθ.  ... 
doi:10.5565/publmat_48104_01 fatcat:rjp2qyvjlbgt7ht7jsnb4fsqka

Problems in infinite graph theory with finite counterpart

Attila Joó, Gábor Sági
He felt that this is not the right innite generalization of the nite theorem and he conjectured the right generalization which was known as the Erd®s-Menger conjecture.  ...  Berger proved the Erd®s-Menger conjecture in its full generality in 2009 (see [2] ) which was one of the greatest achievements in the theory of innite graphs.  ...  Let us start with the case n = 0.  ... 
doi:10.15476/elte.2017.025 fatcat:32cj5xgwm5crnnvprdv55qtvge