Parameterized Complexity of Maximum Edge Colorable Subgraph

Akanksha Agrawal, Madhumita Kundu, Abhishek Sahu, Saket Saurabh, Prafullkumar Tale

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


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.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 26th International Conference, COCOON 2020, Proceedings
EditorsDonghyun Kim, R.N. Uma, Zhipeng Cai, Dong Hoon Lee
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages12
ISBN (Print)9783030581497
StatePublished - 1 Jan 2020
Event26th International Conference on Computing and Combinatorics, COCOON 2020 - Atlanta, United States
Duration: 29 Aug 202031 Aug 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12273 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference26th International Conference on Computing and Combinatorics, COCOON 2020
Country/TerritoryUnited States


  • Edge coloring
  • FPT algorithms
  • Kernel lower bound
  • Kernelization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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