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Erdös-Ko-Rado theorem for ladder graphs

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Abstract

For a graph G and an integer r ≥ 1, G is r-EKR if no intersecting family of independent r-sets of G is larger than the largest star (a family of independent r-sets containing some fixed vertex in G), and G is strictly r-EKR if every extremal intersecting family of independent r-sets is a star. Recently, Hurlbert and Kamat gave a preliminary result about EKR property of ladder graphs. They showed that a ladder graph with n rungs is 3-EKR for all n ≥ 3. The present paper proves that this graph is r-EKR for all 1 ≤ r ≤ n, and strictly r-EKR except for r = n − 1.

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Authors and Affiliations

  1. School of Science, Yanshan University, Qinhuangdao, 066004, China

    Yu-shuang Li

  2. Department of Mathematics, Zhejiang Normal University, Jinhua, 321004, China

    Hua-jun Zhang

Authors
  1. Yu-shuang Li
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  2. Hua-jun Zhang
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Correspondence to Hua-jun Zhang.

Additional information

Supported by the National Natural Science Foundation of China (No. 11201409, No. 11371327) and the Natural Science Foundation of Hebei Province of China (No. A2013203009)

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Li, Ys., Zhang, Hj. Erdös-Ko-Rado theorem for ladder graphs. Acta Math. Appl. Sin. Engl. Ser. 30, 583–588 (2014). https://doi.org/10.1007/s10255-014-0404-x

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  • DOI: https://doi.org/10.1007/s10255-014-0404-x

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