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2-connected 7-coverings of 3-connected graphs on surfaces

✍ Scribed by Ken-ichi Kawarabayashi; Atsuhiro Nakamoto; Katsuhiro Ota

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 116 KB
Volume: 43
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10101

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✦ Synopsis

Abstract

An m‐covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3‐connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2‐connected 7‐covering with at most 6__k__ − 12 vertices of degree 7. We also construct, for every surface F^2^ with Euler genus k ≥ 2, a 3‐connected graph G on F^2^ with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6__k__ − 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003

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