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- W4287281641 abstract "In this article we investigate the structure of uniformly $k$-connected and uniformly $k$-edge-connected graphs. Whereas both types have previously been studied independent of each other, we analyze relations between these two classes. We prove that any uniformly $k$-connected graph is also uniformly $k$-edge-connected for $kle 3$ and demonstrate that this is not the case for $k>3$. Furthermore, uniformly $k$-connected and uniformly $k$-edge-connected graphs are well understood for $kle 2$ and it is known how to construct uniformly $3$-edge-connected graphs. We contribute here a constructive characterization of uniformly $3$-connected graphs that is inspired by Tuttes Wheel Theorem. Eventually, these results help us to prove a tight bound on the number of vertices of minimum degree in uniformly $3$-connected graphs." @default.
- W4287281641 created "2022-07-25" @default.
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- W4287281641 date "2021-03-05" @default.
- W4287281641 modified "2023-09-25" @default.
- W4287281641 title "Uniformly connected graphs" @default.
- W4287281641 doi "https://doi.org/10.48550/arxiv.2103.03767" @default.
- W4287281641 hasPublicationYear "2021" @default.
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