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

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Graphs on Surfaces
Connected graph
Covering
Euler
Genus
Spanning Subgraph
Maximum Degree
Graph in graph theory

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

2-connected 7-coverings of 3-connected graphs on surfaces. / Kawarabayashi, Ken Ichi; Nakamoto, Atsuhiro; Ota, Katsuhiro.

In: Journal of Graph Theory, Vol. 43, No. 1, 05.2003, p. 26-36.

Research output: Contribution to journalArticle

Kawarabayashi, Ken Ichi ; Nakamoto, Atsuhiro ; Ota, Katsuhiro. / 2-connected 7-coverings of 3-connected graphs on surfaces. In: Journal of Graph Theory. 2003 ; Vol. 43, No. 1. pp. 26-36.
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