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A lower bound on cochromatic number for line graphs of a kind of graphs

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Abstract

Erdös, Gimbel and Straight (1990) conjectured that if ω(G)<5 and z(G)>3, then z(G)≥χ(G)−2. But by using the concept of edge cochromatic number it is proved that if G is the line graph of a connected triangle-free graph with ω(G)<5 and G≠K 4, then z(G)≥χ(G)−2.

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References

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Authors and Affiliations

  1. College of Mathematics and Information Science, Northwest Normal University, 730070, Gansu, China

    Liu Xinsheng & Chen Xiang’en

  2. College of Computer Science and Information Engineering, Northwest University for Nationalities, 730030, Gansu, China

    Ou Lifeng

Authors
  1. Liu Xinsheng
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  2. Chen Xiang’en
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  3. Ou Lifeng
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Additional information

Supported by the Natural Science Foundation of Gansu Province (3ZS051-A25-025).

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Xinsheng, L., Xiang’en, C. & Lifeng, O. A lower bound on cochromatic number for line graphs of a kind of graphs. Appl. Math. Chin. Univ. 21, 357–360 (2006). https://doi.org/10.1007/s11766-003-0013-6

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  • DOI: https://doi.org/10.1007/s11766-003-0013-6

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