Infinite paths in planar graphs I: Graphs with radial nets
نویسنده
چکیده
Let G be an infinite 4-connected planar graph such that the deletion of any finite set of vertices from G results in exactly one infinite component. Dean et al proved that either G admits a radial net or a special subgraph of G admits a ladder net, and they used these nets to show that G contains a spanning 1-way infinite path. In this paper, we show that if G admits a radial net, then G also contains a spanning 2-way infinite path. This is a step towards a conjecture of Nash-Williams. ∗Partially supported by NSF grant DMS-9970527
منابع مشابه
Infinite paths in planar graphs II, structures and ladder nets
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عنوان ژورنال:
- Journal of Graph Theory
دوره 47 شماره
صفحات -
تاریخ انتشار 2004