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 - 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 -