Towards Nash-Williams orientation conjecture for infinite graphs

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2024-10-08 DOI:10.1002/jgt.23192

Amena Assem

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引用次数: 0

Abstract

In 1960 Nash-Williams proved that an edge-connectivity of $2 k$ is sufficient for a finite graph to have a $k$ -arc-connected orientation. He then conjectured that the same is true for infinite graphs. In 2016, Thomassen, using his own results on the auxiliary lifting graph, proved that $8 k$ -edge-connected infinite graphs admit a $k$ -arc-connected orientation. Here we improve this result for the class of one-ended locally finite graphs and show that an edge-connectivity of $4 k$ is enough in that case. Crucial to this improvement are results presented in a separate paper, by the same author of this paper, on the key concept of the lifting graph, extending results by Ok, Richter, and Thomassen.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .