Abstract
The notion of gregarious cycles in complete multipartite graphs was introduced by Billington and Hoffman in 2003 and was modified later by Billington, Hoffman, and Rodger and by Billington, Smith, and Hoffman.
In this paper, we propose a new definition of gregarious cycles in complete multipartite graphs which generalizes all of the three definitions. With our definition, we can consider gregarious cycles of long length in complete multipartite graphs, and we show some results on the existence of edge-disjoint decompositions of complete multipartite graphs into gregarious long cycles.
This research was supported for two years by Pusan National University Research Grant.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alspach, B., Gavlas, H.: Cycle decompositions of K n and K n  − I. Journal of Combinatorial Theory, Series B 81, 77–99 (2001)
Billington, E.J., Hoffman, D.G.: Decomposition of complete tripartite graphs into gregarious 4-cycles. Discrete Mathematics 261, 87–111 (2003)
Billington, E.J., Hoffman, D.G.: Equipartite and almost-equipartite gregarious 4-cycle systems. Discrete Mathematics 308, 696–714 (2008)
Billington, E.J., Hoffman, D.G., Rodger, C.A.: Resolvable gregarious cycle decompositions of complete equipartite graphs. Discrete Mathematics 308, 2844–2853 (2008)
Billington, E.J., Smith, B.R., Hoffman, D.G.: Equipartite gregarious 6- and 8-cycle systems. Discrete Mathematics 307, 1659–1667 (2007)
Cho, J.R.: A note on decomposition of complete equipartite graphs into gregarious 6-cycles. Bulletin of the Korean Mathematical Society 44, 709–719 (2007)
Cho, J.R., Gould, R.J.: Decompositions of complete multipartite graphs into gregarious 6-cycles using complete differences. Journal of the Korean Mathematical Society 45, 1623–1634 (2008)
Kim, E.K., Cho, Y.M., Cho, J.R.: A difference set method for circulant decompositions of complete partite graphs into gregarious 4-cycles. East Asian Mathematical Journal 26, 655–670 (2010)
Šajna, M.: On decomposiing K n  − I into cycles of a fixed odd length. Descrete Mathematics 244, 435–444 (2002)
Šajna, M.: Cycle decompositions III: complete graphs and fixed length cycles. Journal of Combinatorial Designs 10, 27–78 (2002)
Smith, B.R.: Equipartite gregarious 5-cycle systems and other results. Graphs and Combinatorics 23, 691–711 (2007)
Smith, B.R.: Some gregarious cycle decompositions of complete equipartite graphs. The Electronic Journal of Combinatorics 16(1), Research Paper 135, 17 (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cho, J.R., Park, J., Sano, Y. (2013). Edge-disjoint Decompositions of Complete Multipartite Graphs into Gregarious Long Cycles. 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_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-45281-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-45280-2
Online ISBN: 978-3-642-45281-9
eBook Packages: Computer ScienceComputer Science (R0)