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7. A note on planar graphs with large width parameters and small grid-minors

Author

Ioan Todinca, Alexander Grigoriev, Natalya Usotskaya, Bert Marchal, Quantitative Economics, Externe publicaties SBE, RS: GSBE ETBC, Amsterdam School of Economics (ASE), University of Amsterdam [Amsterdam] (UvA), Laboratoire d'Informatique Fondamentale d'Orléans (LIFO), Ecole Nationale Supérieure d'Ingénieurs de Bourges-Université d'Orléans (UO), ANR-09-BLAN-0159,AGAPE,Algorithmes de graphes parametres et exacts(2009), Todinca, Ioan, and Blanc - Algorithmes de graphes parametres et exacts - - AGAPE2009 - ANR-09-BLAN-0159 - Blanc - VALID

Subjects
Discrete mathematics, Tree-width, Applied Mathematics, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0102 computer and information sciences, 02 engineering and technology, Grid, 01 natural sciences, Graph, Grid-minor, Planar graph, Treewidth, Combinatorics, symbols.namesake, Branch-width, 010201 computation theory & mathematics, 0202 electrical engineering, electronic engineering, information engineering, symbols, Discrete Mathematics and Combinatorics, Embedding, 020201 artificial intelligence & image processing, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

Given a graph G with tree-width @w(G), branch-width @b(G), and side size of the largest square grid-minor @q(G), it is known that @q(G)@[email protected](G)@[email protected](G)[email protected][email protected](G). In this paper, we introduce another approach to bound the side size of the largest square grid-minor specifically for planar graphs. The approach is based on measuring the distances between the faces in an embedding of a planar graph. We analyze the tightness of all derived bounds. In particular, we present a class of planar graphs where @q(G)[email protected](G)

Published
2012

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