On Inverse Chromatic Number problems (Extended abstract)

Chung, Yerim; Culus, Jean François; Demange, Marc

doi:10.1016/j.endm.2010.05.143

Cited by 3 publications

(2 citation statements)

References 15 publications

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“…Finally, note also that the problem under consideration has some natural connections with the inverse chromatic number problem (see [4]). For a graph G and an integer k, this problem consists in modifying the graph as few as possible such that the chromatic number of the resulting graph is at most k. For an interval graph, suppose that the possible modifications of the graph correspond to shifting intervals to the left or to the right in the interval representation.…”

Section: Related Workmentioning

confidence: 99%

Selective Graph Coloring in Some Special Classes of Graphs

Demange

Monnot

Pop³

et al. 2012

Lecture Notes in Computer Science

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Abstract. In this paper, we consider the selective graph coloring problem. Given an integer k ≥ 1 and a graph G = (V, E) with a partition V1, . . . , Vp of V , it consists in deciding whether there exists a set V * in G such that |V * ∩ Vi| = 1 for all i ∈ {1, . . . , p}, and such that the graph induced by V * is k-colorable. We investigate the complexity status of this problem in various classes of graphs.

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Section: Related Workmentioning

confidence: 99%

Selective Graph Coloring in Some Special Classes of Graphs

Demange

Monnot

Pop³

et al. 2012

Lecture Notes in Computer Science

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“…Main reference includes the following: Orlin, 2000, 2001;Burkard et al, 2008;Burton and Toint 1992;Demange, 2008, 2012;Heuberger, 2004). The inverse number problems have been studied for some NP-hard optimization problems such as the maximum independent set problem ) and the minimum graph coloring problem (Chung et al, , 2010.…”

Section: Introductionmentioning

confidence: 99%

Inverse Bin-packing Number Problems: NP-Hardness and Approximation Algorithms

Chung

2012

Management Science and Financial Engineering

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In the bin-packing problem, we deal with how to pack the items by using a minimum number of bins. In the inverse bin-packing number problem, IBPN for short, we are given a list of items and a fixed number of bins. The objective is to perturb at the minimum cost the item-size vector so that all items can be packed into the prescribed number of bins. We show that IBPN is NP-hard and provide an approximation algorithm. We also consider a variant of IBPN where the prescribed solution value should be returned by a pre-selected specific approximation algorithm.

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