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 - https://www.scopus.com/pages/publications/85091122208
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 -