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A graph is inductive k-independent if there exists an ordering of its vertices v1, ..., vn such that α(G[N (vi)∩Vi]) ≤ k where N (vi) is the neighbourhood of vi, Vi = {vi, ..., vn} and α is the independence number. In this article we design a polynomial time approximation algorithm with ratio ∆/ log(log(∆)/(k + 1)) for the maximum clique problem and also… (More)

2 3 −approximation matching algorithm is sub-exponential. Abstract Mann et al. [11] designed the first algorithm computing a maximal matching that is a 2 3-approximation of the maximum matching in 2 O(n) moves. However, the complexity tightness was not proved. In this paper, we exhibit a sub-exponential execution of this matching algorithm : this algorithm… (More)

- Johanne Cohen, Khaled Maâmra, George Manoussakis, Laurence Pilard
- 2016

2 3 −approximation matching algorithm is sub-exponential. Abstract Manne et al. [11] designed the first algorithm computing a maximal matching that is a 2 3-approximation of the maximum matching in 2 O(n) moves. However, the complexity tightness was not proved. In this paper, we exhibit a sub-exponential execution of this matching algorithm : this algorithm… (More)

Del Pia and Michini recently improved the upper bound of kd due to Klein-schmidt and Onn for the largest possible diameter of the convex hull of a set of points in dimension d whose coordinates are integers between 0 and k. We introduce Euler polytopes which include a family of lattice polytopes with diameter (k + 1)d/2, and thus reduce the gap between the… (More)

A graph is k-degenerate if any induced subgraph has a vertex of degree at most k. In this paper we prove new algorithms finding cliques and similar structures in these graphs. We design linear time Fixed-Parameter Tractable algorithms for induced and non induced bicliques. We prove an algorithm listing all maximal bicliques in time O(k 3 (n − k)2 k),… (More)

A graph is k-degenerate if there exists an ordering of its vertices it was proved that the largest possible number of maximal cliques in an n-vertex k-degenerate graph is (n − k)3 k/3. Then the authors prove an algorithm listing all the maximal cliques of these graphs in optimal time O(k(n − k)3 k/3). In this paper we prove another optimal algorithm.

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