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Boundary Classes of Planar Graphs

Published online by Cambridge University Press:  01 March 2008

VADIM LOZIN
VADIM LOZIN*
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK (e-mail: [email protected])
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Abstract

We analyse classes of planar graphs with respect to various properties such as polynomial-time solvability of the dominating set problem or boundedness of the tree-width. A helpful tool to address this question is the notion of boundary classes. The main result of the paper is that for many important properties there are exactly two boundary classes of planar graphs.

Type
Paper
Information
Combinatorics, Probability and Computing , Volume 17 , Issue 2 , March 2008 , pp. 287 - 295
Copyright
Copyright © Cambridge University Press 2007

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References

[1]Alekseev, V. E. (2003) On easy and hard hereditary classes of graphs with respect to the independent set problem. Discrete Appl. Math. 132 17–26.CrossRefGoogle Scholar
[2]Bodlaender, H. L. and Thilikos, D. M. (1997) Treewidth for graphs with small chordality. Discrete Appl. Math. 79 45–61.CrossRefGoogle Scholar
[3]Boliac, R. and Lozin, V. (2003) Independent domination in finitely defined classes of graphs. Theoret. Comput. Sci. 301 271–284.CrossRefGoogle Scholar
[4]Courcelle, B. and Olariu, S. (2000) Upper bounds to the clique-width of a graph. Discrete Appl. Math. 101 77–114.CrossRefGoogle Scholar
[5]Demaine, E. D. and Hajiaghayi, M. T. (2004) Diameter and treewidth in minor-closed graph families, revisited. Algorithmica 40 211–215.CrossRefGoogle Scholar
[6]Kobler, D. and Rotics, U. (2003) Finding maximum induced matchings in subclasses of claw-free and P 5-free graphs, and in graphs with matching and induced matching of equal maximum size. Algorithmica 37 327–346.CrossRefGoogle Scholar
[7]Korobitsyn, D. V. (1990) On the complexity of determining the domination number in monogenic classes of graphs. Diskret. Mat. 2 90–96 (in Russian). Translation in Discrete Math. Appl. 2 191–199 (1992).CrossRefGoogle Scholar
[8]Lozin, V. (2002) On maximum induced matchings in bipartite graphs. Inform. Process. Lett. 81 7–11.CrossRefGoogle Scholar
[9]Lozin, V. and Rautenbach, D. (2004) On the band-, tree- and clique-width of graphs with bounded vertex degree. SIAM J. Discrete Math. 18 195–206.CrossRefGoogle Scholar
[10]Lozin, V. and Rautenbach, D. (2006) On the tree- and clique-width of bipartite graphs in special classes. Australas. J. Combin. 34 57–67.Google Scholar
[11]Murphy, O. J. (1992) Computing independent sets in graphs with large girth. Discrete Appl. Math. 35 167–170.CrossRefGoogle Scholar
[12]Oum, S.-i. (2005) Rank-width and vertex-minors. J. Combin. Theory Ser. B 95 79–100.CrossRefGoogle Scholar
[13]Yannakakis, M. and Gavril, F. (1980) Edge dominating sets in graphs. SIAM J. Appl. Math. 38 364–372.CrossRefGoogle Scholar