Abstract
In this paper, we present a necessary and sufficient condition for a bipartite distance-hereditary graph to be Hamiltonian. The result is in some sense similar to the well known Hall’s theorem, which concerns the existence of a perfect matching. Based on the condition we also give a polynomial-time algorithm for the Hamilton cycle problem on bipartite distance-hereditary graphs.
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References
Bandelt, H.-J., Mulder, H.M.: Distance-Hereditary Graphs. Journal of Combinatorial Theory B 41, 182–208 (1986)
Bauer, D., Broersma, H., Schmeichel, E.: Toughness in Graphs A Survey. Graphs and Combinatorics 22, 1–35 (2006)
Cournier, A., Habib, M.: A new linear algorithm for modular decomposition. In: Tison, S. (ed.) CAAP 1994. LNCS, vol. 787, pp. 68–84. Springer, Heidelberg (1994)
Chvátal, V.: Tough graphs and Hamiltonian circuits. Discrete Mathematics 5, 215–228 (1973)
Habib, M., de Montgolfier, F., Paul, C.: A simple linear-time modular decomposition algorithm for graphs, using order extension. In: Hagerup, T., Katajainen, J. (eds.) SWAT 2004. LNCS, vol. 3111, pp. 187–198. Springer, Heidelberg (2004)
Hsieh, S.-Y., Ho, C.-W., Hsu, T.-S., Ko, M.-T.: The problem on distance-hereditary graphs. Discrete Applied Mathematics 154, 508–524 (2006)
Hung, R.-W., Wu, S.-C., Chang, M.-S.: Hamiltonian cycle problem on distance-hereditary graphs. Journal of Information Science and Engineering 19, 827–838 (2003)
Hung, R.-W., Chang, M.-S.: Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs. Theoretical Computer Science 341, 411–440 (2005)
Kratsch, D., Lehel, J., Müller, H.: Toughness, hamiltonicity and split graphs. Discrete Mathematics 150, 231–245 (1996)
McConnell, R.M., Mehlhorn, K., Näher, S., Schweitzer, P.: Certifying Algorithms. Computer Science Review 5, 119–161 (2011)
McConnell, R.M., Spinrad, J.P.: Linear-time modular decomposition and efficient transitive orientation of comparability graphs. In: Proceeding SODA, pp. 536–545 (1994)
Müller, H., Nicolai, F.: Polynomial time algorithms for Hamiltonian problems on bipartite distance-hereditary graphs. Information Processing Letters 46, 225–230 (1993)
Müller, H.: Hamiltonian circuits in chordal bipartite graphs. Discrete Mathematics 156, 291–298 (1996)
Nicolai, F.: Hamiltonian problems on distance-hereditary graphs, Technique Report SM-DU-264, Gerhard-Mercator University, Germany (1994)
Tedder, M., Corneil, D.G., Habib, M., Paul, C.: Simpler linear-time modular decomposition via recursive factorizing permutations. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008, Part I. LNCS, vol. 5125, pp. 634–645. Springer, Heidelberg (2008)
Möhring, R.H., Radermacher, F.J.: Substitution decomposition for discrete structures and connections with combinatorial optimization. Annals of Discrete Mathematics 19, 257–356 (1984)
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Takasuga, M., Hirata, T. (2013). A Necessary and Sufficient Condition for a Bipartite Distance-Hereditary Graph to Be Hamiltonian. In: Akiyama, J., Kano, M., Sakai, T. (eds) Computational Geometry and Graphs. TJJCCGG 2012. Lecture Notes in Computer Science, vol 8296. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45281-9_14
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DOI: https://doi.org/10.1007/978-3-642-45281-9_14
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