Testing bipartiteness of geometric intersection graphs

David Eppstein
2009 ACM Transactions on Algorithms  
We show how to test the bipartiteness of an intersection graph of n line segments or simple polygons in the plane, or of balls in R^d, in time O(n log n). More generally we find subquadratic algorithms for connectivity and bipartiteness testing of intersection graphs of a broad class of geometric objects. For unit balls in R^d, connectivity testing has equivalent randomized complexity to construction of Euclidean minimum spanning trees, and hence is unlikely to be solved as efficiently as
more » ... iteness testing. For line segments or planar disks, testing k-colorability of intersection graphs for k>2 is NP-complete.
doi:10.1145/1497290.1497291 fatcat:md4v3ip5hzfchgy2wilggzpgyu