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arXiv:1106.2533v1[cs.DM]13Jun2011 Obstructions for linear rankwidth at most 1

Summary: arXiv:1106.2533v1[cs.DM]13Jun2011
Obstructions for linear rankwidth at most 1
Isolde Adler
, Arthur M. Farley
, Andrzej Proskurowski
June 14, 2011
We provide a characterization of graphs of linear rankwidth at most 1
by minimal excluded vertex-minors.
1 Introduction
The definition and study of various width parameters of graphs has influenced
research on structural characterizations and exploring complexity and algorith-
mic properties of graph classes with bounded width. One of the first such
parameters was bandwidth, discussed for instance in papers by Monien and
Sudborough [8], Chinn et al [4], Assman et al [1]. The first modern width
parameter was treewidth defined by Robertson and Seymour [12], opening the
floodgates for various graph decomposition schemes that define other width pa-
rameters. These parameters have strong impact on complexity of many discrete
optimization problems.
Rankwidth was first defined by Oum and Seymour [11] with the goal of


Source: Adler, Isolde - Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt am Main


Collections: Computer Technologies and Information Sciences