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On 2–Factors with Prescribed Properties in a Bipartite Graph

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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.

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Authors and Affiliations

  1. School of Mathematics and Systems Science, Shandong University, Jinan 250100, P. R. China

    Jin Yan & Gui Zhen Liu

Authors
  1. Jin Yan
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  2. Gui Zhen Liu
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Corresponding author

Correspondence to Jin Yan.

Additional information

This work is supported by NNSF of China (10471078) and Higher Education of MOE, P. R. C. (2004042204)

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Yan, J., Liu, G.Z. On 2–Factors with Prescribed Properties in a Bipartite Graph. Acta Math Sinica 22, 1115–1120 (2006). https://doi.org/10.1007/s10114-005-0666-6

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  • DOI: https://doi.org/10.1007/s10114-005-0666-6

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