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On superperfection of edge-intersection graphs of paths

Abstract : The Routing and Spectrum Assignment problem in Flexgrid Elastic Optical Networks can be modeled in two phases: a selection of paths in the network and an interval coloring problem in the edge-intersection graph of these paths. The interval chromatic number equals the smallest size of a spectrum such that a proper interval coloring is possible, the weighted clique number is a natural lower bound. Graphs where both parameters coincide for all induced subgraphs and for all possible integral weights are called superperfect. We examine the question which minimal non-superperfect graphs can occur in the edge-intersection graphs of paths in different underlying networks and show that for any possible network (even if it is restricted to a path) the resulting edge-intersection graphs are not necessarily superperfect.
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Contributor : Annegret Wagler Connect in order to contact the contributor
Submitted on : Friday, April 26, 2019 - 11:16:06 AM
Last modification on : Friday, April 1, 2022 - 3:10:27 AM


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Hervé Kerivin, Annegret K. Wagler. On superperfection of edge-intersection graphs of paths. CTW 2020, Sep 2020, online, Italy. ⟨10.1007/978-3-030-63072-0_7⟩. ⟨hal-02017433v2⟩



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