Ghoshal, S and Louis, A and Raychaudhury, R
(2019)
*Approximation algorithms for partially colorable graphs.*
In: 22nd International Conference on Approximation Algorithms for Combinatorial Optimization Problems and 23rd International Conference on Randomization and Computation, APPROX/RANDOM 2019, 20 - 22 September 2019, Cambridge.

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## Abstract

Graph coloring problems are a central topic of study in the theory of algorithms. We study the problem of partially coloring partially colorable graphs. For α ≤ 1 and k ∈ Z+, we say that a graph G = (V, E) is α-partially k-colorable, if there exists a subset S ⊂ V of cardinality |S| ≥ α|V | such that the graph induced on S is k-colorable. Partial k-colorability is a more robust structural property of a graph than k-colorability. For graphs that arise in practice, partial k-colorability might be a better notion to use than k-colorability, since data arising in practice often contains various forms of noise. We give a polynomial time algorithm that takes as input a (1 − ∊)-partially 3-colorable graph G and a constant γ ∈ [∊, 1/10], and colors a (1 − ∊/γ) fraction of the vertices using Õ (Formula presented.) colors. We also study natural semi-random families of instances of partially 3-colorable graphs and partially 2-colorable graphs, and give stronger bi-criteria approximation guarantees for these family of instances.

Item Type: | Conference Paper |
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Publication: | Leibniz International Proceedings in Informatics, LIPIcs |

Publisher: | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |

Additional Information: | The copyright for this article belongs to Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. |

Keywords: | Approximation algorithms; Combinatorial optimization; Computation theory; Graphic methods; Polynomial approximation; Random processes, Bi-criteria; Cardinalities; Colorability; Graph coloring problem; Polynomial-time algorithms; Semi-random; Semi-random models; Vertex coloring, Graph theory |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 07 Jan 2023 05:01 |

Last Modified: | 07 Jan 2023 05:01 |

URI: | https://eprints.iisc.ac.in/id/eprint/78845 |

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