| On 2-Factors with Prescribed Properties in a Bipartite Graph |
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| 作者姓名： | Jin YAN Gui Zhen LIU |
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| 作者单位： | School of Mathematics and Systems Science, Shandong University, Jinan 250100, P. R. China |
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| 基金项目： | This work is supported by NNSF of China （10471078） and Higher Education of M0E, P. R. C. （2004042204） |
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| 摘 要： | Liu and Yan gave the degree condition for a balanced bipartite graph G = （V1, V2; E） to have k vertex-disjoint quadrilaterals containing any given k independent edges e1,……, ek of G, respectively. They also conjectured that for any k independent edges e1,……, ek of G, G has a 2-factor with k cycles C1, C2, ……, Ck with respect to {e1, e2,……, ek} such that k - 1 of them are quadrilaterals. In this paper, we prove this conjecture.
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| 关 键 词： | 双向图 顶点不相交 四边形 双因子 |
| 收稿时间： | 2003-12-29 |
| 修稿时间： | 2003-12-292004-11-25 |
On 2–Factors with Prescribed Properties in a Bipartite Graph |
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| Jin YAN Gui Zhen LIU.On 2-Factors with Prescribed Properties in a Bipartite Graph[J].Acta Mathematica Sinica,2006,22(4):1115-1120. |
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| Authors: | Jin Yan Gui Zhen Liu |
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| Institution: | (1) School of Mathematics and Systems Science, Shandong University, Jinan 250100, P. R. China |
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| Abstract: | Liu and Yan gave the degree condition for a balanced bipartite graph G = (V
1, V
2;E) to have k vertex–disjoint quadrilaterals containing any given k independent edges e
1, . . . , e
k
of G, respectively. They also conjectured that for any k independent edges e
1, . . . , e
k
of G, G has a 2–factor with k cycles C
1,C
2, . . . , C
k
with respect to {e
1, e
2, . . . , e
k
} such that k–1 of them are quadrilaterals. In this paper, we prove this conjecture.
This work is supported by NNSF of China (10471078) and Higher Education of MOE, P. R. C. (2004042204) |
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| Keywords: | Bipartite graph Vertex-disjoint Quadrilateral 2-Factor |
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