Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Bounding the Search Number of Graph Products

  • Received : 2017.02.18
  • Accepted : 2018.07.04
  • Published : 2019.03.23
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Abstract

In this paper, we provide results for the search number of the Cartesian product of graphs. We consider graphs on opposing ends of the spectrum: paths and cliques. Our main result determines the pathwidth of the product of cliques and provides a lower bound for the search number of the product of cliques. A consequence of this result is a bound for the search number of the product of arbitrary graphs G and H based on their respective clique numbers.

Keywords

GBDHBF_2019_v59n1_175_f0001.png 이미지

Figure 1: An illustration highlighting bags B1, B2, B3, and Bn, following the decomposition of Theorem 3.8.

GBDHBF_2019_v59n1_175_f0002.png 이미지

Figure 2: An illustration highlighting some bags described by (3.2) following the decomposition of Theorem 3.9.

GBDHBF_2019_v59n1_175_f0003.png 이미지

Figure 3: An illustration highlighting some bags described by (3.3) and (3.4) following the decomposition of Theorem 3.9.

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