Obstructions for linear rank-width at most 1
نویسندگان
چکیده
منابع مشابه
Obstructions for linear rankwidth at most 1
We provide a characterization of graphs of linear rankwidth at most 1 by minimal excluded vertex-minors.
متن کاملExcluded vertex-minors for graphs of linear rank-width at most k
Linear rank-width is a graph width parameter, which is a variation of rank-width by restricting its tree to a caterpillar. As a corollary of known theorems, for each k, there is a finite obstruction set Ok of graphs such that a graph G has linear rank-width at most k if and only if no vertex-minor of G is isomorphic to a graph in Ok. However, no attempts have been made to bound the number of gr...
متن کاملAn Upper Bound on the Size of Obstructions for Bounded Linear Rank-Width
We provide a doubly exponential upper bound in p on the size of forbidden pivot-minors for symmetric or skew-symmetric matrices over a fixed finite field F of linear rank-width at most p. As a corollary, we obtain a doubly exponential upper bound in p on the size of forbidden vertex-minors for graphs of linear rank-width at most p. This solves an open question raised by Jeong, Kwon, and Oum [Ex...
متن کاملLinear rank-width of distance-hereditary graphs II. Vertex-minor obstructions
In the companion paper [Linear rank-width of distance-hereditary graphs I. A polynomialtime algorithm, Algorithmica 78(1):342–377, 2017], we presented a characterization of the linear rank-width of distance-hereditary graphs, from which we derived an algorithm to compute it in polynomial time. In this paper, we investigate structural properties of distance-hereditary graphs based on this charac...
متن کاملAlgorithms and obstructions for linear-width and related search parameters
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 for...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.05.001