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2‐connected 7‐coverings of 3‐connected graphs on surfaces
Authors:Ken‐ichi Kawarabayashi  Atsuhiro Nakamoto  Katsuhiro Ota
Abstract:
An mcovering 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 6k ? 12 vertices of degree 7. We also construct, for every surface F2 with Euler genus k ≥ 2, a 3‐connected graph G on F2 with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6k ? 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003
Keywords:3‐connected graph  2‐connected subgraph  surface  representativity
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