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Edge-reconstruction of planar graphs with minimum valency 5

✍ Scribed by Josef Lauri

Publisher
John Wiley and Sons
Year
1979
Tongue
English
Weight
780 KB
Volume
3
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

The object of this paper is to show tht every planar graph of minimum valency 5 is reconstructible from its family of edge‐deleted subgraphs.

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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

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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.

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## Abstract This paper presents two tight inequalities for planar graphs of minimum degree five. An edge or face of a plane graph is light if the sum of the degrees of the vertices incident with it is small. A light edge inequality is presented which shows that planar graphs of minimum degree five

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## Abstract A graph __H__ is light in a given class of graphs if there is a constant __w__ such that every graph of the class which has a subgraph isomorphic to __H__ also has a subgraph isomorphic to __H__ whose sum of degrees in __G__ is ≀ __w__. Let $\cal G$ be the class of simple planar graphs