In this paper, we investigate the well-studied Hamiltonian cycle problem, and present an interesting dichotomy result on split graphs. T. Akiyama, T. Nishizeki, and N. Saito [23] have shown that the Hamiltonian cycle problem is NP-complete in planar bipartite graph with maximum degree 3. Using this reduction, we show that the Hamiltonian cycle problem is NP-complete in split graphs. In particular, we show that the problem is NP-complete in K1,5-free split graphs. Further, we present polynomial-time algorithms for Hamiltonian cycle in K1, 3- free and K1,4-free split graphs. We believe that the structural results presented in this paper can be used to show similar dichotomy result for Hamiltonian path and other variants of Hamiltonian cycle problem.
CITATION STYLE
Renjith, P., & Sadagopan, N. (2017). Hamiltonicity in split graphs - A dichotomy. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10156 LNCS, pp. 320–331). Springer Verlag. https://doi.org/10.1007/978-3-319-53007-9_28
Mendeley helps you to discover research relevant for your work.