Clustered planarity: small clusters in Eulerian graphs

Authors:
Eva Jelínková;Jan Kára;Jan Kratochvíl;Martin Pergel;Ondřej Suchý;Tomáš Vyskočil
Affiliations:
Department of Applied Mathematics, Charles University, Praha, Czech Republic;Institute for Theoretical Computer Science, Charles University, Praha, Czech Republic;Department of Applied Mathematics, Charles University, Praha, Czech Republic and Institute for Theoretical Computer Science, Charles University, Praha, Czech Republic;Department of Applied Mathematics, Charles University, Praha, Czech Republic;Department of Applied Mathematics, Charles University, Praha, Czech Republic;Department of Applied Mathematics, Charles University, Praha, Czech Republic
Venue:
GD'07 Proceedings of the 15th international conference on Graph drawing
Year:
2007

Citing 3
Cited 5

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Abstract

We present several polynomial-time algorithms for c-planarity testing for clustered graphs with clusters of size at most three. The most general result concerns a special class of Eulerian graphs, namely graphs obtained froma fixed-size 3-connected graph bymultiplying and then subdividing edges. We further give algorithms for 3-connected graphs, and for graphs with small faces. The last result applies with no restrictions on the cluster size.