document: Embeddings of planar graphs that minimize the number of long-face cycles We consider the problem of finding embeddings of planar graphs that minimize the number of long-face cycles . We prove that for any k > or = 4 , it is NP-complete to find an embedding that minimizes the number of face cycles of length at least k
doc_bio_tags: B O B I O O O O O O O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
extractive_keyphrases: embeddings planar graphs
abstractive_keyphrases: long-face cycles np-complete problem graph drawing