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A characterization of the weighted version of McEliece–Rodemich–Rumsey–Schrijver number based on convex quadratic programming

    For any graph G, Luz and Schrijver [A convex quadratic characterization of the Lovász theta number, SIAM J. Discrete Math.19(2) (2005) 382–387] introduced a characterization of the Lovász number ϑ(G) based on convex quadratic programming. A similar characterization is now established for the weighted version of the number ϑ(G), independently introduced by McEliece, Rodemich, and Rumsey [The Lovász bound and some generalizations, J. Combin. Inform. Syst. Sci.3 (1978) 134–152] and Schrijver [A Comparison of the Delsarte and Lovász bounds, IEEE Trans. Inform. Theory25(4) (1979) 425–429]. Also, a class of graphs for which the weighted version of ϑ(G) coincides with the weighted stability number is characterized.

    AMSC: 05C50, 05C69, 90C27, 90C25

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    Published: 21 October 2015

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