Skip to main content Accessibility help
×
Home
Hostname: page-component-857cdc78dc-89p7v Total loading time: 0.222 Render date: 2022-05-16T06:56:02.110Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

Boundary Classes of Planar Graphs

Published online by Cambridge University Press:  01 March 2008

VADIM LOZIN*
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK (e-mail: V.Lozin@warwick.ac.uk)

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
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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 1726.CrossRefGoogle Scholar
[2]Bodlaender, H. L. and Thilikos, D. M. (1997) Treewidth for graphs with small chordality. Discrete Appl. Math. 79 4561.CrossRefGoogle Scholar
[3]Boliac, R. and Lozin, V. (2003) Independent domination in finitely defined classes of graphs. Theoret. Comput. Sci. 301 271284.CrossRefGoogle Scholar
[4]Courcelle, B. and Olariu, S. (2000) Upper bounds to the clique-width of a graph. Discrete Appl. Math. 101 77114.CrossRefGoogle Scholar
[5]Demaine, E. D. and Hajiaghayi, M. T. (2004) Diameter and treewidth in minor-closed graph families, revisited. Algorithmica 40 211215.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 327346.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).Google Scholar
[8]Lozin, V. (2002) On maximum induced matchings in bipartite graphs. Inform. Process. Lett. 81 711.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 195206.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 5767.Google Scholar
[11]Murphy, O. J. (1992) Computing independent sets in graphs with large girth. Discrete Appl. Math. 35 167170.CrossRefGoogle Scholar
[12]Oum, S.-i. (2005) Rank-width and vertex-minors. J. Combin. Theory Ser. B 95 79100.CrossRefGoogle Scholar
[13]Yannakakis, M. and Gavril, F. (1980) Edge dominating sets in graphs. SIAM J. Appl. Math. 38 364372.CrossRefGoogle Scholar
11
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Boundary Classes of Planar Graphs
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Boundary Classes of Planar Graphs
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Boundary Classes of Planar Graphs
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *