منابع مشابه
Rank-width and vertex-minors
The rank-width is a graph parameter related in terms of fixed functions to cliquewidth but more tractable. Clique-width has nice algorithmic properties, but no good “minor” relation is known analogous to graph minor embedding for tree-width. In this paper, we discuss the vertex-minor relation of graphs and its connection with rank-width. We prove a relationship between vertex-minors of bipartit...
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 کاملGraphs of Small Rank-width Are Pivot-minors of Graphs of Small Tree-width
We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...
متن کاملGraphs of Small Rank-width are Pivot-minors of Graphs of Small Tree-width
We prove that every graph of rank-width k is a pivot-minor of a graph of tree-width at most 2k. We also prove that graphs of rank-width at most 1, equivalently distance-hereditary graphs, are exactly vertex-minors of trees, and graphs of linear rank-width at most 1 are precisely vertex-minors of paths. In addition, we show that bipartite graphs of rank-width at most 1 are exactly pivot-minors o...
متن کاملSim-width and induced minors
We introduce a new graph width parameter, called special induced matching width, shortly sim-width, which does not increase when taking induced minors. For a vertex partition (A,B) of a graphG, this parameter is based on the maximum size of an induced matching {a1b1, . . . , ambm} in G where a1, . . . , am ∈ A and b1, . . . , bm ∈ B. Classes of graphs of bounded sim-width are much wider than cl...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2005
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2005.03.003