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Remarks on Path-transitivity in Finite Graphs

โœ 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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๐Ÿ“œ SIMILAR VOLUMES


On paths in planar graphs
โœ Sanders, Daniel P. ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 93 KB ๐Ÿ‘ 2 views

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.

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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

On Finite s-Transitive Graphs of Odd Ord
โœ Cai Heng Li ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 128 KB

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.

A theorem on paths in planar graphs
โœ Norishige Chiba; Takao Nishizeki ๐Ÿ“‚ Article ๐Ÿ“… 1986 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 108 KB ๐Ÿ‘ 1 views

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.

A theorem on paths in planar graphs
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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.