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- W49648587 abstract "Graphs and Algorithms 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." @default.
- W49648587 created "2016-06-24" @default.
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- W49648587 date "2008-01-01" @default.
- W49648587 modified "2023-10-18" @default.
- W49648587 title "On the k-restricted structure ratio in planar and outerplanar graphs" @default.
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- W49648587 doi "https://doi.org/10.46298/dmtcs.423" @default.
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