Browse > Article
http://dx.doi.org/10.7858/eamj.2013.024

ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES  

Kim, Seong Kun (School of General Studies, Kangwon National University)
Publication Information
East Asian mathematical journal / v.29, no.3, 2013 , pp. 337-347 More about this Journal
Abstract
For an even integer m at least 4 and any positive integer $t$, it is shown that the complete equipartite graph $K_{km(2t)}$ can be decomposed into edge-disjoint gregarious m-cycles for any positive integer ${\kappa}$ under the condition satisfying ${\frac{{(m-1)}^2+3}{4m}}$ < ${\kappa}$. Here it will be called a gregarious cycle if the cycle has at most one vertex from each partite set.
Keywords
cycle; decomposition; complete multipartite graph; gregarious; complete equipartite graph;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 B. Alspach and H. Gavlas, Cycle decompositions of $K_n$ and $K_n-I$. J. Combin. Theory Ser. B 81(2001), 77-99.   DOI   ScienceOn
2 E. Billington and D. G. Ho man, Decomposition of complete tripartite graphs into gre-garious 4-cycles. Discrete Math. 261(2003), 87-111.   DOI   ScienceOn
3 E. Billington and D. G. Ho man, Equipartite and almost-equipartite gregarious 4-cycle systems. Discrete Math. 308(2008), 696-714.   DOI   ScienceOn
4 E. Billington, D. G. Ho man and C. A. Rodger, Resolvable gregarious cycle decompo-sitions of complete equipartite graphs. Discrete Math. 308(2008), 2844-2853.   DOI   ScienceOn
5 E. Billington, B. Smith and D. G. Ho man, Equipartite gregarious 6- and 8-cycle systems Discrete Math. 307(2007), 1659-1667.   DOI   ScienceOn
6 N. J. Cavenagh and E. J. Billington, Decompositions of complete multipartite graphs into cycles of even length. Graphs and Combinatorics 16(2000), 49-65.   DOI
7 J. R. Cho, A note on decomposition of complete equipartite graphs into gregarious 6-cycles. Bull. Korean Math. Soc. 44(2007), 709-719.   과학기술학회마을   DOI   ScienceOn
8 J. R. Cho and S. K. Kim, Decompositions of $K_{km+1(2t)}$ into Gregarious m-cycles using Difference Sets. Preprint.
9 J. R. Cho, M. J. Ferrara, R. J. Gould and J. R. Schmitt, A difference set method for circular decompositions of complete mutipartite graphs into gregarious 4-cycles. Preprint.
10 J. R. Cho and R. J. Gould, Decompositions of complete multipartite graphs into gregarious 6-cycles using complete differences. J. Korean Math. Soc. 45(2008), 1623-1634.   과학기술학회마을   DOI   ScienceOn
11 M. Sajna, On decomposiing $K_n-I$ into cycles of a fixed odd length. Descrete Math. 244(2002), 435-444.   DOI   ScienceOn
12 M. Sajna, Cycle decompositions III: complete graphs and fixed length cycles. J. Combin. Designs 10(2002), 27-78.   DOI   ScienceOn
13 Benjamin R. Smith, Some gregarious cycle decompositions of complete equipartite graph. E. J. of Combinatorics 16(1) (2009), R135.