A geometric graph is a graph embedded in the plane in such a way that vertices correspond to points in general position and edges correspond to segments connecting the appropriate points. A noncrossing Hamiltonian path in a geometric graph is a Hamiltonian path which does not contain any intersecting pair of edges. In the paper, we study a problem asked by Micha Perles: Determine a function h, where h(n) is the largest number k such that when we remove arbitrary set of k edges from a complete geometric graph on n vertices, the resulting graph still has a noncrossing Hamiltonian path. We prove that h(n) = Ω(√n). We also determine the function exactly in case when the removed edges form a star or a matching, and give asymptotically tight bounds in case they form a clique. © Springer-Verlag 2004.
CITATION STYLE
Černý, J., Dvořák, Z., Jelínek, V., & Kára, J. (2004). Noncrossing Hamiltoniaii Paths in Geometric Graphs. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2912, 86–97. https://doi.org/10.1007/978-3-540-24595-7_8
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