Exploiting Sparsity for Bipartite Hamiltonicity

Author Andreas Björklund

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Andreas Björklund
  • Department of Computer Science, Lund University, Sweden

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Andreas Björklund. Exploiting Sparsity for Bipartite Hamiltonicity. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 3:1-3:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


We present a Monte Carlo algorithm that detects the presence of a Hamiltonian cycle in an n-vertex undirected bipartite graph of average degree delta >= 3 almost surely and with no false positives, in (2-2^{1-delta})^{n/2}poly(n) time using only polynomial space. With the exception of cubic graphs, this is faster than the best previously known algorithms. Our method is a combination of a variant of Björklund's 2^{n/2}poly(n) time Monte Carlo algorithm for Hamiltonicity detection in bipartite graphs, SICOMP 2014, and a simple fast solution listing algorithm for very sparse CNF-SAT formulas.

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ACM Subject Classification
  • Mathematics of computing → Graph algorithms
  • Hamiltonian cycle
  • bipartite graph


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  1. Andreas Björklund. Determinant Sums for Undirected Hamiltonicity. SIAM J. Comput., 43(1):280-299, 2014. URL: http://dx.doi.org/10.1137/110839229.
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