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The sandwich line-graph

Cornaz, Denis; Meurdesoif, Philippe (2010), The sandwich line-graph, Electronic Notes in Discrete Mathematics, 36, 1, p. 955-960. http://dx.doi.org/10.1016/j.endm.2010.05.121

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Type
Article accepté pour publication ou publié
Date
2010
Journal name
Electronic Notes in Discrete Mathematics
Volume
36
Number
1
Publisher
Elsevier
Pages
955-960
Publication identifier
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Author(s)
Cornaz, Denis

Meurdesoif, Philippe
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
Subjects / Keywords
Lovász theta function; auxiliary line graph; Graph coloring