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Upper embeddability, edge independence number and girth

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Abstract

Combined with the edge-connectivity, this paper investigates the relationship between the edge independence number and upper embeddability. And we obtain the following result:

Let G be a k-edge-connected graph with girth g. If

$$ \alpha '(G) \leqslant ((k - 2)^2 + 2)\left\lfloor {\frac{g} {2}} \right\rfloor + \frac{{1 - ( - 1)^g }} {2}((k - 1)(k - 2) + 1) - 1, $$

where k = 1, 2, 3, and α′(G) denotes the edge independence number of G, then G is upper embeddable and the upper bound is best possible. And it has generalized the relative results.

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Authors and Affiliations

  1. Department of Mathematics, Hunan Normal University, Changsha, 410081, China

    ZhangDong Ouyang, Ling Tang & YuanQiu Huang

Authors
  1. ZhangDong Ouyang
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  2. Ling Tang
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  3. YuanQiu Huang
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Corresponding author

Correspondence to ZhangDong Ouyang.

Additional information

This work was supported by National Natural Science Foundation of China (Grant No. 10771062) and New Century Excellent Talents in University (Grant No. NCET-07-0276)

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Ouyang, Z., Tang, L. & Huang, Y. Upper embeddability, edge independence number and girth. Sci. China Ser. A-Math. 52, 1939–1946 (2009). https://doi.org/10.1007/s11425-009-0002-1

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  • DOI: https://doi.org/10.1007/s11425-009-0002-1

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