Generating cycle spaces for graphs on surfaces with small genera

Authors:
Han Ren;Yanpei Liu;D. J. Ma;J. J. Lu
Affiliations:
Department of Mathematics, East China Normal University, Shanghai 200062, China;Department of Mathematics, Northern Jiaotong University, Beijing 100044, China;Department of Mathematics, East China Normal University, Shanghai 200062, China;Department of Mathematics, East China Normal University, Shanghai 200062, China
Venue:
European Journal of Combinatorics
Year:
2004

Citing 4
Cited 0

A polynomial-time algorithm to find the shortest cycle basis of a graph

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Embeddings of graphs with no short noncontractible cycles

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When do short cycles generate the cycle space?

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Graph Theory With Applications

Graph Theory With Applications

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Abstract

In this paper we investigate cycle base structures of a 2-(edge)-connected graph on surfaces with small genera and show that short cycles do generate the cycle spaces in the case of "small face-embeddings". Examples show that the conditions in our main results are best possible. As applications we find the exact formulae for the minimum lengths of cycle bases of some types of graphs which conclude several known results. Finally, we generalize those results for graphs embedded on general orientable surfaces.