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 -