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Colouring polygon visibility graphs and their generalizations

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 نشر من قبل Bartosz Walczak
 تاريخ النشر 2021
  مجال البحث الهندسة المعلوماتية
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Curve pseudo-visibility graphs generalize polygon and pseudo-polygon visibility graphs and form a hereditary class of graphs. We prove that every curve pseudo-visibility graph with clique number $omega$ has chromatic number at most $3cdot 4^{omega-1}$. The proof is carried through in the setting of ordered graphs; we identify two conditions satisfied by every curve pseudo-visibility graph (considered as an ordered graph) and prove that they are sufficient for the claimed bound. The proof is algorithmic: both the clique number and a colouring with the claimed number of colours can be computed in polynomial time.



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