A Note on Fractional Coloring and the Integrality gap of LP for Maximum Weight Independent Set

• Published in: Electronic notes in discrete mathematics Vol. 55; pp. 113 - 116
• Main Authors: Chalermsook, Parinya, Vaz, Daniel
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2016; Elsevier
• Subjects: Computer Science; Discrete Mathematics; Fractional coloring; linear programming; maximum weight independent set; Fractional coloring; linear programming; maximum weight independent set; Maximum weight independent set; Linear programming

We prove a tight connection between two important notions in combinatorial optimization. Let G be a graph class (i.e. a subset of all graphs) and r(G)=supG∈G⁡χf(G)ω(G) where χf(G) and ω(G) are the fractional chromatic number and clique number of G respectively. In this note, we prove that r(G) tight...