Crossing-free subgraphs

M. Ajtai, V. Chvátal, M. M. Newborn, E. Szemerédi

Research output: Contribution to journalArticle

75 Citations (Scopus)


If m⩾4 then every planar drawing of a graph with n vertices and m edges contains more than m3/100n2 edge-crossings and fewer than 1013n crossing-free subgraphs. The first result settles a conjecture of Erdös and Guy and the second result settles a conjecture of Newborn and Moser.

Original languageEnglish
Pages (from-to)9-12
Number of pages4
JournalNorth-Holland Mathematics Studies
Issue numberC
Publication statusPublished - Jan 1 1982


ASJC Scopus subject areas

  • Mathematics(all)

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