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

2004
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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 ...##
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Page 4624 of Mathematical Reviews Vol. , Issue 90H
[page]

1990
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Mathematical Reviews
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. (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 ...##
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Page 1341 of Mathematical Reviews Vol. , Issue 85d
[page]

1985
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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 ...

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Enlarging vertex-flames in countable digraphs
[article]

2021
*
arXiv
*
pre-print

A structural generalisation of vertex-flames and largeness to infinite digraphs was given by

arXiv:2003.06178v2
fatcat:b7lm6gkdljah5hmj2tjmqb53ry
*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. ...##
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Large vertex-flames in uncountable digraphs
[article]

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 ...

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

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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. ...##
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Hausdorff dimension, projections, and the Fourier transform

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. ...

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Problems in infinite graph theory with finite counterpart

2017

He felt that this is not

doi:10.15476/elte.2017.025
fatcat:32cj5xgwm5crnnvprdv55qtvge
*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. ...