In this paper we prove this result for planar graphs achieving g(k) = 2O(k). Our bound is radically better than the bounds known for general graphs. Moreover, ...
A subdivided grid is a graph obtained from a grid by replacing some edges of the grid by pairwise internally vertex disjoint paths of length at least one.
A subdivided grid is a graph obtained from a grid by replacing some edges of the grid by pairwise internally vertex disjoint paths of length at least one. Embed ...
In this paper we prove this result for planar graphs achieving g(k) = 2O(k). Our bound is radically better than the bounds known for general graphs. Moreover, ...
Mar 21, 2023 · Bibliographic details on Tight Bounds for Linkages in Planar Graphs.
Mar 4, 2022 · A cut in a triangulation can't use all three edges of a face, so an upper bound is two edges from each face. This is achieved by triangulations ...
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Jun 15, 2017 · The maximum number of edges in a planar graph with n vertices is achieved when every face is a triangle. In this case 2E=3F by double counting.
Nov 29, 2019 · Abstract page for arXiv paper 1911.13161: Tight Bounds for Planar Strongly Connected Steiner Subgraph with Fixed Number of Terminals (and ...
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This implies that the Feldman-Ruhl algorithm for DSN is optimal, even on planar directed acyclic graphs. As in our lower bound for planar SCSS, the proof is by ...
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Our algorithm for planar directed graphs can be generalized to graphs excluding a fixed minor. In general graphs, we cannot hope for such a dramatic improvement ...