Gruia Călinescu ; Cristina G. Fernandes - On the k-restricted structure ratio in planar and outerplanar graphs

dmtcs:423 - Discrete Mathematics & Theoretical Computer Science, January 1, 2008, Vol. 10 no. 3 - https://doi.org/10.46298/dmtcs.423
On the k-restricted structure ratio in planar and outerplanar graphsArticle

Authors: Gruia Călinescu 1; Cristina G. Fernandes ORCID2

  • 1 Departement of Computer Science [UIC]
  • 2 Department of Computer Science

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1 = 2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.


Volume: Vol. 10 no. 3
Section: Graph and Algorithms
Published on: January 1, 2008
Imported on: March 26, 2015
Keywords: [INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]
Funding:
    Source : OpenAIRE Graph
  • Approximation Algorithms for Networks; Funder: National Science Foundation; Code: 0515088

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