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A note on decomposition of complete equipartite graphs into gregarious $6$-cycles

조정래
대한수학회 (The Korean Mathematical Society)|2007.11|대한수학회보 (Bulletin of the KMS)|제44권 제4호|pp. 709-719

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Abstract

In [8], it is shown that the complete multipartite graphK n (2t)having n partite sets of size 2t, wheren 6 and t 1, has a decompo-sition into gregarious 6-cycles ifn 0;1;3 or 4 (mod 6). Here, a cycleis called gregarious if it has at most one vertex from any particular par-tite set. In this paper, whenn 0 or 3 (mod 6), another method usingdierence set is presented. Furthermore, whenn 0 (mod 6), the de-composition obtained in this paper is 1 -circular, in the sense that it isinvariant under the mapping which keeps the partite set which is indexedby 1 xed and permutes the remaining partite sets cyclically.

참고문헌 (10)

  1. "Cycle decompositions of K n and K n I", B81(1), pp.77~99 (2001)
  2. "Decomposition of complete tripartite graphs into gre-garious 4-cycles", 261(1-3), pp.87~111 (2003)
  3. "Resolvable gregarious cycle decompo-sitions of complete equipartite graphs"
  4. "Decomposition of complete multipartite graphs intocycles of even length", 16(1), pp.49~65 (2000)
  5. "Graphs & digraphs: Fourth edition" (2005), Chapman &Hall[DOI]
  6. "A dierence set method for cir-cular decompositions of complete mutipartite graphs into gregarious 4-cycles"
  7. "Decompositions of complete multipartite graphs into gregar-ious 6-cycles using dierence sets To appear in J A NOTE ON DECOMPOSITION OF COMPLETE EQUIPARTITE GRAPHS 719"
  8. "The equipartite Oberwolfach problem with uniform tables", A101(1), pp.20~34 (2003)
  9. "A generalization of the Oberwolfach problem and Ct-factorizations of completeequipartite graphs", 8(1), pp.42~49 (2000)
  10. "On decomposing K n I into cycles of a xed odd length", 244(1-3), pp.435~444 (2002)

관련 논문AI추천

ON DECOMPOSITIONS OF THE COMPLETE EQUIPARTITE GRAPHS Kkm(2t) INTO GREGARIOUS m-CYCLES김성근영남수학회 · East Asian Mathematical Journal2013 · 제29권 제3호Circulant Decompositions of Certain Multipartite Graphs into Gregarious Cycles of a Given Length조정래영남수학회 · East Asian Mathematical Journal2014 · 제30권 제3호A REMARK ON CIRCULANT DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS BY GREGARIOUS CYCLES조정래영남수학회 · East Asian Mathematical Journal2017 · 제33권 제1호DECOMPOSITIONS OF COMPLETE MULTIPARTITE GRAPHS INTO GREGARIOUS 6-CYCLES USING COMPLETE DIFFERENCES조정래, Ronald J. Gould대한수학회 · 대한수학회지2008 · 제45권 제6호A difference set method for circulant decompositions of complete partite graphs into gregarious 4-cycles김은경, 조영민, 조정래영남수학회 · East Asian Mathematical Journal2010 · 제26권 제5호Existence of cyclic 50-cycle systems of the complete bipartite graph K_n,nH. Shen, Y. Ji, Y. Zheng장전수학회 · Advanced Studies in Contemporary Mathematics2007 · 제14권 제1호

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