The rank-width of the square grid

  • Authors:

  • Vít Jelínek

  • Affiliations:

  • Department of Applied Mathematics, Charles University, Prague, Czech Republic

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2010

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Abstract

Rank-width is a graph width parameter introduced by Oum and Seymour. It is known that a class of graphs has bounded rank-width if, and only if, it has bounded clique-width, and that the rank-width of G is less than or equal to its branch-width. The nxnsquare grid, denoted by G"n","n, is a graph on the vertex set {1,2,...,n}x{1,2,...,n}, where a vertex (x,y) is connected by an edge to a vertex (x^',y^') if and only if |x-x^'|+|y-y^'|=1. We prove that the rank-width of G"n","n is equal to n-1, thus solving an open problem of Oum.