TY - GEN

T1 - Large Independent Sets in Subquartic Planar Graphs

AU - Mnich, Matthias

PY - 2016

Y1 - 2016

N2 - By the famous four color theorem, every planar graph admits an independent set that contains at least one quarter of its vertices. This lower bound is tight for infinitely many planar graphs, and finding maximum independent sets in planar graphs is \mathsf {np}\mathsf {np}-hard. A well-known open question in the field of parameterized complexity asks whether the problem of finding a maximum independent set in a given planar graph is fixed-parameter tractable, for parameter the “gain” over this tight lower bound. This open problem has been posed many times [4, 8, 10, 13, 17, 20, 31, 32, 35, 38].we show fixed-parameter tractability of the independent set problem parameterized above tight lower bound in planar graphs with maximum degree at most 4, in subexponential time.

AB - By the famous four color theorem, every planar graph admits an independent set that contains at least one quarter of its vertices. This lower bound is tight for infinitely many planar graphs, and finding maximum independent sets in planar graphs is \mathsf {np}\mathsf {np}-hard. A well-known open question in the field of parameterized complexity asks whether the problem of finding a maximum independent set in a given planar graph is fixed-parameter tractable, for parameter the “gain” over this tight lower bound. This open problem has been posed many times [4, 8, 10, 13, 17, 20, 31, 32, 35, 38].we show fixed-parameter tractability of the independent set problem parameterized above tight lower bound in planar graphs with maximum degree at most 4, in subexponential time.

U2 - 10.1007/978-3-319-30139-6_17

DO - 10.1007/978-3-319-30139-6_17

M3 - Conference article in proceeding

SN - 978-3-319-30138-9

T3 - Lecture Notes in Computer Science

SP - 209

EP - 221

BT - WALCOM: Algorithms and Computation

A2 - Kaykobad, Mohammed

A2 - Petreschi, Rossella

PB - Springer

ER -