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.
Remarks on Path-transitivity in Finite Graphs
โ Scribed by Marston D.E. Conder; Cheryl E. Praeger
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 244 KB
- Volume
- 17
- Category
- Article
- ISSN
- 0195-6698
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๐ SIMILAR VOLUMES
The automorphism-group of an infinite graph acts in a natural way on the set of d-fibers (components of the set of rays with respect to the Hausdorff metric). For connected, locally finite, almost transitive graphs the kernel of this action is proved to be the group of bounded automorphisms. This co
It is shown that, for a positive integer s, there exists an s-transitive graph of odd order if and only if s 3 and that, for s=2 or 3, an s-transitive graph of odd order is a normal cover of a graph for which there is an automorphism group that is almost simple and s-transitive.
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.
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.