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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 O k 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 O k. However, no attempts… (More)

Given n subspaces of a finite-dimensional vector space over a fixed finite field F, we wish to find a linear layout V1, V2,. .. , Vn of the subspaces such that dim((V1 +V2 +· · ·+Vi)∩(Vi+1 +· · ·+Vn)) ≤ k for all i; such a linear layout is said to have width at most k. When restricted to 1-dimensional subspaces, this problem is equivalent to computing the… (More)

We give alternative definitions for maximum matching width, e.g. a graph G has mmw(G) ≤ k if and only if it is a subgraph of a chordal graph H and for every maximal clique X of H there exists A, B, C ⊆ X with A∪B ∪C = X and |A|, |B|, |C| ≤ k such that any subset of X that is a minimal separator of H is a subset of either A, B or C. Treewidth and branchwidth… (More)

A homogeneous set of a graph G is a set X of vertices such that 2 ≤ |X| < |V (G)| and no vertex in V (G) − X has both a neighbor and a non-neighbor in X. A graph is prime if it has no homogeneous set. We present an algorithm to decide whether a class of graphs given by a finite set of forbidden induced subgraphs contains infinitely many non-isomorphic prime… (More)

The maximum matching width is a width-parameter that is defined on a branch-decomposition over the vertex set of a graph. The size of a maximum matching in the bipartite graph is used as a cut-function. In this paper, we characterize the graphs of maximum matching width at most 2 using the minor obstruction set. Also, we compute the exact value of the… (More)

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