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On minors of graphs with at least 3n −4 edges

✍ Scribed by M. Khalifat; Themistocles Politof; A. Satyanarayana

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
390 KB
Volume
17
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A point disconnecting set S of a graph G is a nontrivial m‐separator, where m = |S|, if the connected components of G ‐ S can be partitioned into two subgraphs, each of which has at least two points. A 3‐connected graph is quasi 4‐connected if it has no nontrivial 3‐separators. Suppose G is a graph having n ≥ 6 points. We prove three results: (1) If G is quasi 4‐connected with at least 3__n__ ‐ 4 edges, then the graph K^−^~1~, obtained from K~6~ by deleting an edge, is a minor of G. (2) If G has at least 3__n__ ‐ 4 edges then either K^−^~6~ or the graph obtained by pasting two disjoint copies of K~5~ together along a triangle is a minor of G. (3) If the minimum degree of G is at least 6, then K^−^~6~ is a minor of G. © 1993 John Wiley & Sons, Inc.

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