Algorithms and obstructions for linear-width and related search parameters

  title={Algorithms and obstructions for linear-width and related search parameters},
  author={Dimitrios M. Thilikos},
  journal={Discrete Applied Mathematics},
The linear-width of a graph G is de ned to be the smallest integer k such that the edges of G can be arranged in a linear ordering (e1; : : : ; er) in such a way that for every i = 1; : : : ; r 1, there are at most k vertices incident to edges that belong both to fe1; : : : ; eig and to fei+1; : : : ; erg. In this paper, we give a set of 57 graphs and prove that it is the set of the minimal forbidden minors for the class of graphs with linear-width at most two. Our proof also gives a linear… CONTINUE READING
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