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Clustering powers of sparse graphs

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 نشر من قبل Micha{\\l} Pilipczuk
 تاريخ النشر 2020
  مجال البحث الهندسة المعلوماتية
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We prove that if $G$ is a sparse graph --- it belongs to a fixed class of bounded expansion $mathcal{C}$ --- and $din mathbb{N}$ is fixed, then the $d$th power of $G$ can be partitioned into cliques so that contracting each of these clique to a single vertex again yields a sparse graph. This result has several graph-theoretic and algorithmic consequences for powers of sparse graphs, including bounds on their subchromatic number and efficient approximation algorithms for the chromatic number and the clique number.



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