We prove a theorem on paths with prescribed ends in a planar graph which extends Tutte's theorem on cycles in planar graphs [9] and implies the conjecture of Plummer (51 asserting that every 4-connected planar graph is Hamiltonian-connected.
A theorem on paths in planar graphs
β Scribed by Norishige Chiba; Takao Nishizeki
- Publisher
- John Wiley and Sons
- Year
- 1986
- Tongue
- English
- Weight
- 108 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0364-9024
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β¦ Synopsis
C. Thomassen extended Tutte's theorem on cycles in planar graphs in the paper "A Theorem on Paths in Planar Graphs". This note corrects a flaw in his proof.
π SIMILAR VOLUMES
This paper generalizes a theorem of Thomassen on paths in planar graphs. As a corollary, it is shown that every 4-connected planar graph has a Hamilton path between any two specified vertices x, y and containing any specified edge other than xy.
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
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
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