A note on packing paths in planar graphs
✍ Scribed by András Frank; Zoltán Szigeti
- Publisher
- Springer-Verlag
- Year
- 1995
- Tongue
- English
- Weight
- 506 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0025-5610
No coin nor oath required. For personal study only.
📜 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.
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.
Some new properties of the distribution of elements and vertices with respect to the windows of a connected planar graph G are established. It is also shown that a window matrix of G has properties similar to the properties of an incidence matrix of a graph which is not necessarily planar. A method