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Creators/Authors contains: "Dibek, Cemil"

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  1. ; ; ; (, Mathematics of Operations Research)
    We give a combinatorial polynomial-time algorithm to find a maximum weight independent set in perfect graphs of bounded degree that do not contain a prism or a hole of length four as an induced subgraph. An even pair in a graph is a pair of vertices all induced paths between which are even. An even set is a set of vertices every two of which are an even pair. We show that every perfect graph that does not contain a prism or a hole of length four as an induced subgraph has a balanced separator which is the union of a bounded number of even sets, where the bound depends only on the maximum degree of the graph. This allows us to solve the maximum weight independent set problem using the well-known submodular function minimization algorithm. Funding: This work was supported by the Engineering and Physical Sciences Research Council [Grant EP/V002813/1]; the National Science Foundation [Grants DMS-1763817, DMS-2120644, and DMS-2303251]; and Alexander von Humboldt-Stiftung. 
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    Free, publicly-accessible full text available February 1, 2026
  2. ; ; ; ; ; ; (, Journal of Combinatorial Theory, Series B)
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  3. ; ; ; ; ; (, Journal of Combinatorial Theory, Series B)
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  4. ; ; (, Discrete Mathematics)
    null (Ed.)
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  5. ; (, Journal of Graph Theory)
    Abstract A graph isstrongly perfectif every induced subgraph of it has a stable set that meets every maximal clique of . A graph isclaw‐freeif no vertex has three pairwise nonadjacent neighbors. The characterization of claw‐free graphs that are strongly perfect by a set of forbidden induced subgraphs was conjectured by Ravindra in 1990 and was proved by Wang in 2006. Here we give a shorter proof of this characterization. 
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