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I have graph. I need visualise it with nodes arranged in a circle. How can i khow it's possible circle visualisation without intersections of edges or not?

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Smells like an NP-hard/NP-complete problem, but I could be wrong. You could try asking on cstheory.stackexchange.comMarkus Jarderot

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You can use planarity testing to check if a graph can be laid out on a plane without intersections.