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A level graph G = (V,E, λ) is a graph with a mapping λ : V → {1, . . . , k}, k ≥ 1, that partitions the vertex set V as V = V1 ∪ . . . ∪ Vk, Vj = λ−1(j), Vi ∩ Vj = ∅ for i ̸= j, such that λ(v) = λ(u) + 1 for each edge (u, v) ∈ E. Thus a level planar graph can be drawn with the vertices of every Vj , 1 ≤ j ≤ k, placed on a horizontal line, representing the… (More)

- Katharina Hammersen, Bert Randerath
- Australasian J. Combinatorics
- 2013

The notion of mirror nodes, first introduced by Fomin, Grandoni and Kratsch in 2006, turned out to be a useful item for their design of an algorithm for the maximum independent set problem (MIS). Given two nodes u, v of a graph G = (V, E) with distG(u, v) = 2, u is called a mirror of v if N(v) \N(u) induces a (possibly empty) clique. In order to have a well… (More)

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