It is shown that a 3-connected planar graph with minimum valency 4 is edge-reconstructible if no 4-vertex is adjacent to a 5-vertex. ## 1. Introduction In this paper, all graphs G=(V(G),E(G)) considered will be finite and simple. A connected graph G is said to have connectivity k o = ko(G) if the
On 4-critical planar graphs with high edge density
β Scribed by Gerhard Koester
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 236 KB
- Volume
- 98
- Category
- Article
- ISSN
- 0012-365X
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β¦ Synopsis
Koester, G., On 4-critical planar graphs with high edge density, Discrete Mathematics 98 (1991) 147-151.
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On graphs critical with respect to edge-colourings, Discrete Math. 37 (1981) 289-296. The error occurs in the proof of Case 2 of Theorem 5 (p. 294). We now revise the proof for Case 1 (p. 293) and Case 2 (p. 294) as follows: Case 1: jI # p. In this case, the terminal vertex of the (1, p)-chain with
An edge e of a finite and simple graph G is called a fixed edge of G if G -e + e' ~G implies e' = e. In this paper, we show that planar graphs with minimum degree 5 contain fixed edges, from which we prove that a class of planar graphs with minimum degree one is edge reconstructible.
## Abstract A point disconnecting set __S__ of a graph __G__ is a nontrivial __m__βseparator, where __m__ = |__S__|, if the connected components of __G__ β __S__ can be partitioned into two subgraphs, each of which has at least two points. A 3βconnected graph is quasi 4βconnected if it has no nontr