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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2010.1
- 수록면
- 655 - 670 (16page)
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초록· 키워드
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The complete multipartite graph $K_{n(m)}$ with $n\geq 4$ partite sets of size $m$ is shown to have a decomposition into $4$-cycles in such a way that vertices of each cycle belong to distinct partite sets of $K_{n(m)}$, if 4 divides the number of edges. Such cycles are called {\it gregarious}, and were introduced by Billington and Hoffman (\cite{BH}) and redefined in \cite{BH2}. We independently came up with the result of \cite{BH2} by using a difference set method, and improved the result so that the composition is circulant, in the sense that it is invariant under the cyclic permutation of partite sets. The composition is then used to construct gregarious $4$-cycle decompositions when one partite set of the graph has different cardinality than that of others. Some results on joins of decomposable complete multipartite graphs are also presented.
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참고문헌 (11)
참고문헌 신청
B. Alspach / 2001 / Cycle decompositions of Kn and Kn / J. Combin. Theory Ser. B 81 : 77 ~ 99
D. Sotteau / 1981 / Decomposition of into cycles (circuits) of length 2k / J. Combin. Theory Ser. B 30 : 75 ~ 81
E. Billington / 2003 / Decomposition of complete tripartite graphs into gre-garious 4-cycles / Discrete Math 261 : 87 ~ 111
E. Billington / 2008 / Equipartite and almost-equipartite gregarious 4-cycle decompositions / Discrete Math. 308 (5) : 696 ~ 714
E. Billington / 2008 / Resolvable gregarious cycle decompo-sitions of complete equipartite graphs / Discrete Math. 308 (13) : 2844 ~ 2853
D. Sotteau / 1981 / Decomposition of into cycles (circuits) of length 2k / J. Combin. Theory Ser. B 30 : 75 ~ 81
E. Billington / 2003 / Decomposition of complete tripartite graphs into gre-garious 4-cycles / Discrete Math 261 : 87 ~ 111
E. Billington / 2008 / Equipartite and almost-equipartite gregarious 4-cycle decompositions / Discrete Math. 308 (5) : 696 ~ 714
E. Billington / 2008 / Resolvable gregarious cycle decompo-sitions of complete equipartite graphs / Discrete Math. 308 (13) : 2844 ~ 2853
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