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

Ken Ichi Kawarabayashi, Atsuhiro Nakamoto, Katsuhiro Ota

Research output: Contribution to journalArticle

5 Citations (Scopus)

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 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.

Original languageEnglish
Pages (from-to)26-36
Number of pages11
JournalJournal of Graph Theory
Volume43
Issue number1
DOIs
Publication statusPublished - 2003 May

ASJC Scopus subject areas

  • Geometry and Topology

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