Abstract
In this paper, we investigate Hamiltonian path problem in the context of split graphs and produce a dichotomy result on the complexity of the problem. That is, unless P = NP, Hamiltonian path problem has no polynomial-time solution in \(K_{1,5}\)-free split graphs and polynomial-time solvable in \(K_{1,4}\)-free split graphs.
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References
Broersma, H.J.: On some intriguing problems in hamiltonian graph theory - a survey. Discrete Math. 251(1), 47–69 (2002)
Gould, R.J.: Advances on the Hamiltonian problem - a survey. Graphs Comb. 19(1), 7–52 (2003)
Bertossi, A.A., Bonuccelli, M.A.: Hamiltonian circuits in interval graph generalizations. Inf. Process. Lett. 23(4), 195–200 (1986)
Muller, H.: Hamiltonian circuits in chordal bipartite graphs. Discrete Math. 156(1), 291–298 (1996)
Garey, M.R., Johnson, D.S., Tarjan, R.E.: Planar hamiltonian circuit problem is NP-complete. SIAM J. Comput. 5(4), 704–714 (1976)
Gordon, V.S., Orlovich, Y.L., Werner, F.: Hamiltonian properties of triangular grid graphs. Discrete Math. 308(24), 6166–6188 (2008)
Keil, J.M.: Finding Hamiltonian circuits in interval graphs. Inf. Process. Lett. 20(4), 201–206 (1985)
Shih, W.K., Chern, T.C., Hsu, W.L.: An O(\(n^{2}\)log n) algorithm for the Hamiltonian cycle problem on circular-arc graphs. SIAM J. Comput. 21(6), 1026–1046 (1992)
Renjith, P., Sadagopan, N.: Hamiltonicity in split graphs - a dichotomy. In: Gaur, D., Narayanaswamy, N.S. (eds.) CALDAM 2017. LNCS, vol. 10156, pp. 320–331. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-53007-9_28
West, D.B.: Introduction to Graph Theory. Prentice Hall of India, New Delhi (2003)
Renjith, P., Sadagopan, N.: Hamiltonian path in split graphs - a dichotomy. In: arXiv (2017)
Akiyama, T., Nishizeki, T., Saito, N.: NP-completeness of the Hamiltonian cycle problem for bipartite graphs. J. Inf. Process. 3(2), 73–76 (1980)
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Renjith, P., Sadagopan, N. (2018). Hamiltonian Path in \(K_{1,t}\)-free Split Graphs- A Dichotomy. In: Panda, B., Goswami, P. (eds) Algorithms and Discrete Applied Mathematics. CALDAM 2018. Lecture Notes in Computer Science(), vol 10743. Springer, Cham. https://doi.org/10.1007/978-3-319-74180-2_3
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DOI: https://doi.org/10.1007/978-3-319-74180-2_3
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