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Covering contractible edges in 3-connected graphs. II. Characterizing those with covers of size three

✍ Scribed by Robert L. Hemminger; Xingxing Yu

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

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✦ Synopsis

Abstract

It is shown that if G is a 3‐connected graph with |V(G)| ≥ 10, then, with the exception of one infinite class based on K~3,p~, it takes at least four vertices to cover the set of contractible edges of G. © 1993 John Wiley & Sons, Inc.

📜 SIMILAR VOLUMES

Covering contractible edges in 3-connect
Covering contractible edges in 3-connected graphs. I: Covers of size three are cutsets
✍ Akira Saito 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 397 KB 👁 1 views

## Abstract An edge of a 3‐connected graph is said to be __contractible__ if its contraction results in a 3‐connected graph. In this paper, a covering of contractible edges is studied. We give an alternative proof to the result of Ota and Saito (__Scientia__ (A) 2 (1988) 101–105) that the set of co

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✍ Xingxing Yu 📂 Article 📅 1994 🏛 John Wiley and Sons 🌐 English ⚖ 493 KB 👁 1 views

## Abstract In this paper, we show that if a 3‐connected graph __G__ other than __K__~4~ has a vertex subset __K__ that covers the set of contractible edges of __G__ and if |__K__| 3 and |__V(G)__| 3|__K__| − 1, then __K__ is a cutset of __G__. We also give examples to show that this result is best