How unique is Lovász's theta function?

Abstract : The famous Lovász's ϑ function is computable in polynomial time for every graph, as a semi-definite program (Grötschel, Lovász and Schrijver, 1981). The chromatic number and the clique number of every perfect graph G are computable in polynomial time. Despite numerous efforts since the last three decades, stimulated by the Strong Perfect Graph Theo-rem (Chudnovsky, Robertson, Seymour and Thomas, 2006), no combinatorial proof of this result is known. In this work, we try to understand why the "key properties" of Lovász's ϑ function make it so "unique". We introduce an infinite set of convex functions, which includes the clique number ω and ϑ . This set includes a sequence of linear programs which are monotone increasing and converging to ϑ . We provide some evidences that ϑ is the unique function in this setting allowing to compute the chromatic number of perfect graphs in polynomial time.
Complete list of metadatas

Cited literature [13 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01095638
Contributor : Arnaud Pêcher <>
Submitted on : Monday, December 15, 2014 - 11:34:33 PM
Last modification on : Wednesday, February 13, 2019 - 10:32:02 AM
Long-term archiving on : Saturday, April 15, 2017 - 8:49:22 AM

File

pswz_rev.pdf
Files produced by the author(s)

Licence


Distributed under a Creative Commons Attribution - NonCommercial - NoDerivatives 4.0 International License

Identifiers

  • HAL Id : hal-01095638, version 1

Citation

Arnaud Pêcher, Oriol Serra, Annegret K. Wagler, Xuding Zhu. How unique is Lovász's theta function?. VIII ALIO/EURO Workshop on Applied Combinatorial Optimization, Dec 2014, Montevideo, Uruguay. ⟨hal-01095638⟩

Share

Metrics

Record views

2231

Files downloads

551