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The sandwich line-graph

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Date
2010
Dewey
Principes généraux des mathématiques
Sujet
Lovász theta function; auxiliary line graph; Graph coloring
Journal issue
Electronic Notes in Discrete Mathematics
Volume
36
Number
1
Publication date
2010
Article pages
955-960
Publisher
Elsevier
DOI
http://dx.doi.org/10.1016/j.endm.2010.05.121
URI
https://basepub.dauphine.fr/handle/123456789/5025
Collections
  • LAMSADE : Publications
Metadata
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Author
Cornaz, Denis
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Meurdesoif, Philippe
Type
Article accepté pour publication ou publié
Abstract (EN)
We observe that View the MathML source for any graph G with n vertices, where View the MathML source is any acyclic orientation of G and where View the MathML source is the (complement of the) auxiliary line graph introduced in [Cornaz, D., and Jost, V., A one-to-one correspondence between colorings and stable sets, Operations Research Letters 36 (2008), 673–676]. (Where as usual, ω and χ denote the clique number and the chromatic number.) It follows that, for any graph parameter β(G) sandwiched between ω(G) and χ(G), then View the MathML source is sandwiched between ω(G) and χ(G) too. Numerical experiments show that Φtheta is closer to χ than theta, where theta is Lovász theta function

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