An infinite graph is 2-indivisible if the deletion of any finite set of vertices from the graph results in exactly one infinite component. Let G be a 4-connected, 2-indivisible, infinite, plane graph. It is known that G contains a spanning 1-way infinite path. In this paper, we prove a stronger resu
One-way infinite hamiltonian paths in infinite maximal planar graphs
β Scribed by H. -O. Jung
- Book ID
- 112946288
- Publisher
- Vandenhoeck & Ruprecht
- Year
- 1994
- Tongue
- German
- Weight
- 477 KB
- Volume
- 64
- Category
- Article
- ISSN
- 0025-5858
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Let G be a 4connected infinite planar graph such that the deletion of any finite set of vertices of G results in at most one infinite component. We prove a conjecture of Nash-Williams that G has a 1 -way infinite spanning path. 0 1996 John Wiley & Sons, Inc. [7] has shown that every 4-connected fini
## Abstract We prove NashβWilliams' conjecture that every 4βconnected, 3βindivisible, infinite, planar graph contains a spanning 2βway infinite path. A graph is said to be 3βindivisible if the deletion of any finite set of vertices results in at most two infinite components. Β© 2007 Wiley Periodical
Nash-Williams conjectured that a 4-connected infinite planar graph contains a spanning 2-way infinite path if, and only if, the deletion of any finite set of vertices results in at most two infinite components. In this article, we prove this conjecture for graphs with no dividing cycles and for grap