Embedded-width: A variant of treewidth for plane graphs
Glencora Borradaile, Jeff Erickson, Hung Le, Robbie Weber
TL;DR
This paper introduces embedded-width, a new graph parameter for plane graphs that respects their embedding, providing bounds, algorithms, and novel planar graph matching results.
Contribution
It defines embedded-width for plane graphs, establishes bounds relating it to treewidth, and presents a fixed parameter tractable algorithm for its computation.
Findings
Embedded-width is bounded in terms of treewidth.
A fixed parameter tractable algorithm for computing embedded-width.
Novel bounds on matchings in planar graphs.
Abstract
We define a special case of tree decompositions for planar graphs that respect a given embedding of the graph. We study the analogous width of the resulting decomposition we call the embedded-width of a plane graph. We show both upper bounds and lower bounds for the embedded-width of a graph in terms of its treewidth and describe a fixed parameter tractable algorithm to calculate the embedded-width of a plane graph. To do so, we give novel bounds on the size of matchings in planar graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Complexity and Algorithms in Graphs · Interconnection Networks and Systems