2-Connected spanning subgraphs with low maximum degree in locally planar graphs

Authors:
M. N. Ellingham;Ken-ichi Kawarabayashi
Affiliations:
Department of Mathematics, 1326 Stevenson Center, Vanderbilt University, Nashville, TN 37240, USA;National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
Venue:
Journal of Combinatorial Theory Series B
Year:
2007

Citing 13
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2-connected spanning subgraphs of planar 3-connected graphs

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2-connected coverings of bounded degree in 3-connected graphs

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On 2-connected spanning subgraphs with low maximum degree

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Long cycles in graphs on a fixed surface

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Subgraphs of graphs on surfaces with high representativity

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A theorem on paths in locally planar triangulations

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Abstract

In this paper, we prove that there exists a function a:N"0xR"+-N such that for each @e0, if G is a 4-connected graph embedded on a surface of Euler genus k such that the face-width of G is at least a(k,@e), then G has a 2-connected spanning subgraph with maximum degree at most 3 in which the number of vertices of degree 3 is at most @e|V(G)|. This improves results due to Kawarabayashi, Nakamoto and Ota [K. Kawarabayashi, A. Nakamoto, K. Ota, Subgraphs of graphs on surfaces with high representativity, J. Combin. Theory Ser. B 89 (2003) 207-229], and Bohme, Mohar and Thomassen [T. Bohme, B. Mohar, C. Thomassen, Long cycles in graphs on a fixed surface, J. Combin. Theory Ser. B 85 (2002) 338-347].