Abstract.
We prove that the strong product of graphs G 1×⋯×G n is pancyclic, in particular hamiltonian, for n≈cΔ for any cln(25/12)+1/64≈0.75 whenever all G i are connected graphs with the maximum degree at most Δ.
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Acknowledgments.
Our attention to Hamilton cycles in strong graph products was drawn by Moshe Rosenfeld during his stay at Charles University, Prague. The general version of the problem, namely whether strong graph products are pancyclic, was suggested to us by Zdeněk Ryjáček during Graph Theory Day IV held in Prague in February 2001. The research was done as a part of Research Experience for Undergraduates programme 2000. This is a joint programme of DIMACS at Rutgers University and DIMATIA at Charles University. Our REU supervisors were János Komlós and Endre Szemerédi from Rutgers and Jan Kratochvíl and Jaroslav Nešetřil from Charles University. The authors would like to thank the anonymous referee for heplful suggestions and for drawing their attention to the reference [1].
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This research was supported by KONTAKT ME 337 as a part of REU programme and in part by GACR 201/99/0242
The author acknowledges partial support by NSF grant DMS-9900969 and by Institute for Theoretical Computer Science
The author acknowledges partial support by Institute for Theoretical Computer Science
Institute for Theoretical Computer Science is supported by Ministry of Education of Czech Republic as project LN00A056
Final version received: August 6, 2003
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Král, D., Maxová, J., Podbrdský, P. et al. Pancyclicity of Strong Products of Graphs. Graphs and Combinatorics 20, 91–104 (2004). https://doi.org/10.1007/s00373-003-0545-9
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DOI: https://doi.org/10.1007/s00373-003-0545-9