TY - GEN

T1 - Parameterized Complexity of Maximum Edge Colorable Subgraph

AU - Agrawal, Akanksha

AU - Kundu, Madhumita

AU - Sahu, Abhishek

AU - Saurabh, Saket

AU - Tale, Prafullkumar

N1 - Funding Information:
Akanksha Agrawal: Funded by the PBC Fellowship Program for Outstanding PostDoctoral Researchers from China and India. Saket Saurabh: Funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 819416), and Swarnajayanti Fellowship (No DST/SJF/MSA01/2017-18).. Prafullkumar Tale: Funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement SYSTEMATICGRAPH (No. 725978). Most parts of this work was completed when the author was a Senior Research Fellow at The Institute of Mathematical Sciences, HBNI, Chennai, India.
Funding Information:
Prafullkumar Tale: Funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement SYSTEMATICGRAPH (No. 725978). Most parts of this work was completed when the author was a Senior Research Fellow at The Institute of Mathematical Sciences, HBNI, Chennai, India.
Funding Information:
Akanksha Agrawal: Funded by the PBC Fellowship Program for Outstanding PostDoctoral Researchers from China and India. Saket Saurabh: Funded by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 819416), and Swarnajayanti Fellowship (No DST/SJF/MSA01/2017-18).
Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

PY - 2020/1/1

Y1 - 2020/1/1

N2 - A graph H is p-edge colorable if there is a coloring, such that for distinct, we have. The Maximum Edge-Colorable Subgraph problem takes as input a graph G and integers l and p, and the objective is to find a subgraph H of G and a p-edge-coloring of H, such that. We study the above problem from the viewpoint of Parameterized Complexity. We obtain FPT algorithms when parameterized by: (1) the vertex cover number of G, by using Integer Linear Programming, and (2) l, a randomized algorithm via a reduction to Rainbow Matching, and a deterministic algorithm by using color coding, and divide and color. With respect to the parameters, where k is one of the following: (1) the solution size, l, (2) the vertex cover number of G, and (3), where is the size of a maximum matching in G; we show that the (decision version of the) problem admits a kernel with vertices. Furthermore, we show that there is no kernel of size, for any and computable function f, unless NP coNP/poly.

AB - A graph H is p-edge colorable if there is a coloring, such that for distinct, we have. The Maximum Edge-Colorable Subgraph problem takes as input a graph G and integers l and p, and the objective is to find a subgraph H of G and a p-edge-coloring of H, such that. We study the above problem from the viewpoint of Parameterized Complexity. We obtain FPT algorithms when parameterized by: (1) the vertex cover number of G, by using Integer Linear Programming, and (2) l, a randomized algorithm via a reduction to Rainbow Matching, and a deterministic algorithm by using color coding, and divide and color. With respect to the parameters, where k is one of the following: (1) the solution size, l, (2) the vertex cover number of G, and (3), where is the size of a maximum matching in G; we show that the (decision version of the) problem admits a kernel with vertices. Furthermore, we show that there is no kernel of size, for any and computable function f, unless NP coNP/poly.

KW - Edge coloring

KW - FPT algorithms

KW - Kernel lower bound

KW - Kernelization

UR - http://www.scopus.com/inward/record.url?scp=85091122208&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-58150-3_50

DO - 10.1007/978-3-030-58150-3_50

M3 - Conference contribution

AN - SCOPUS:85091122208

SN - 9783030581497

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 615

EP - 626

BT - Computing and Combinatorics - 26th International Conference, COCOON 2020, Proceedings

A2 - Kim, Donghyun

A2 - Uma, R.N.

A2 - Cai, Zhipeng

A2 - Lee, Dong Hoon

PB - Springer Science and Business Media Deutschland GmbH

T2 - 26th International Conference on Computing and Combinatorics, COCOON 2020

Y2 - 29 August 2020 through 31 August 2020

ER -