A Fast Algorithm for the Product Structure of Planar Graphs

DOI10.1007/S00453-020-00793-5arXiv2004.02530MaRDI QIDQ6338144

Pat Morin

Publication date: 6 April 2020

Abstract: Dujmovi'c et al (FOCS2019) recently proved that every planar graph $G$ is a subgraph of $$, where $$ denotes the strong graph product, $H$ is a graph of treewidth 8 and $P$ is a path. This result has found numerous applications to linear graph layouts, graph colouring, and graph labelling. The proof given by Dujmovi'c et al is based on a similar decomposition of Pilipczuk and Siebertz (SODA2019) which is constructive and leads to an $O(n^2)$ time algorithm for finding $H$ and the mapping from $V(G)$ onto $$. In this note, we show that this algorithm can be made to run in $O(nlogn)$ time.

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Planar graphs; geometric and topological aspects of graph theory (05C10) Structural characterization of families of graphs (05C75) Graph algorithms (graph-theoretic aspects) (05C85) Graph operations (line graphs, products, etc.) (05C76)

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